Inspired by the Luftwaffe thread. Germany have historically been a land power, and were only powerful at sea for a brief decade in the early 20th Century. Their performance in WW2 was poor, in part due to the fact that Hitler concentrated on the Heer and the LW. Their major surface combatants were the Bismarck and Scharnost-class battleships, the Deutschland-class pre-Dreadnoughts, the Deutschland and Admiral Hipper-class Heavy Cruisers/Panzerschiffe and the Emden, Konigsberg and Leipzig-class Light Cruisers. They also had 30 destroyers and plenty of smaller craft. They are most famous for their U-Boats, which were revolutionary and the only successful branch of the KM.
Hitler ordered the Plan Z naval construction plan in 1939. It projected a navy of 10 battleships, 3 battlecruisers, 4 Aircraft Carriers, 15 Panzerschiffe, 5 Heavy Cruisers, 13 Light Cruisers, 22 Scout ships, 68 Destroyers and 90 Torpedo Boats. While this would be no Royal, Imperial Japanese or US Navy, it would undoubtedly be the 4th best navy in the world.
Now, this plan isn't really what the KM needs so what would be the best POD to get the strongest possible Kriegsmarine in 1940?
I don't have the time nor umph to finish this right now, so I'll just say that this is just a start. Additionally, I won't give anything like a complete OOB for the KM, but rather work towards setting the stage for others, so to speak. So on to the first part of my reply...
Let's divide up the build up into some categories, like pre-nazi, pre-hitler, pre/post ToV getting short shrift. For me, the OTL German rearmament program tried to take massive amounts of manpower from the populace, and turn them into military forces that needed to achieve proficiency in certain tasks, like sailors or pilots, and this of course took time and money. What if, however, we start off by trying to get at least some of these needed personnel the required skills sets, but not by draining the budget, or at least offsetting this to a large degree, by making them into profit making professionals? Increasing the overall budget, by investing in money making ventures, means reducing the cost of rearmament programs later on, and having more money for that, as well.
First, we need the pre-Nazi German government to be working even more than in OTL, to get around every restriction of the ToV, as soon and as thoroughly as possible. Much of this will need to be done in secret, as there just is no way to build up a navy, starting in the 1920's, and NOT be noticed to be in violation of the ToV. Some things can be done as historically, like building aircraft and submarines in other countries is a start.
For the strongest possible Kriegsmarine by 1940, Germany is going to need 10,000's of trained and seasoned sailors, and for this they need ships years and decades earlier than OTL. These ships cannot be warships, but can they be merchant ships, and thus not fall under the evil that was the ToV? Can Pre-Nazi Germany buy ships in foreign lands?
Merchantmen:
Probably the most important type of vessel that the Pre-Nazi German government can build from 1919-1939, is a vast merchant marine fleet, because unlike anything else built, these can actually make a profit, rather than being a drain on the German economy from the time they are laid down all the way up to the outbreak of hostilities. Even if, for some unfathomable reason, they fail to make a profit, their losses will be far less than any other preparation made in the 1920's, and will allow Germany to acquire large numbers of trained and seasoned sailors, for years before war clouds even begin to darken the farthest horizons. Will doing such set off alarms in some places, yes, but will this be enough to see the public in such nations see this a such a threat that they need to fund any kind of naval shipbuilding programs whatsoever, almost certainly not. My reasoning here is that, foreign populations will be asking themselves, why do we, an already heavily taxed population, need to be willing to be bilked out of MORE, just because the Germans are building a large fleet of merchantmen, especially when, in any future war, they will either be rusting away in some port or other around the world, of even better, captured and used by us?
Submarines:
Is an unarmed merchant submarine a violation of the ToV? I think a German built/owned /operated one should not be see as such {Except by the French, of course}, but to be safe, have such built in foreign shipyards {not just in the Netherlands} and gain needed expertise/experience operating such vessels by the 1930's. You don't need any large number of such ships, but you do need to constantly be pushing the tonnage up, such that you can have as large and long ranged a cargo submarine as possible, as soon as possible. Being seen to be making small profits, or suffering small losses would be ideal, with the justification that never again will Germany have her people starved in time of war. Of course, Germany is never going to be able to feed her population by using some fictional supersized merchant submarine fleet, but a very small number of such vessels could supply Germany's war industries with needed rare materials quite nicely. And of course, if you have an operation class of very large, very long ranged, unarmed submarines, building additional units, for a very different purpose, and of a slightly modified design, could have interesting effects for any future war.
Once Germany can openly shrug off the ToV, they should begin building whatever submarines they like in public, in small numbers, while gearing up to build vast numbers on the down low.
Floatplanes:
With the massive merchantmen construction program in the 1920's and 1930's, there should be a secret law passed, that requires that every single German merchantman be equipped with one or more floatplanes, and that these must, whenever possible, be launched and recovered during the regular voyages of every such ship, on every such voyage, for the entire interwar period. This program can be thinly disguised as being about such pedestrian needs as mail delivery, harbor pilot shuttling, or other equally pedestrian uses. Such a vast, far reaching program will come at a cost, but if such a cost can just be billed to the profits of the merchant ships voyages, then Germany can gain much needed pilots, well trained and seasoned, long before any new war... This of course would require that the ship's crew were also experienced with launching/recovering such aircraft, as well as with their repair and maintenance issues, as well as any issues with the aircrafts reliability. It would also give perfect cover for photographing ports and harbors, all around the world, such that the next time Germany finds itself in a war, they will have a vast stockpile of aerial photographs of virtually every commercial shipping location ever visited by a German merchantman over the last 15 or so years, with the obvious impact such intel could have in helping plan visits of a less friendly nature...
Seaplanes:
In addition to the one engined floatplanes carried aboard ship, the Germans would do well to invest heavily in seaplanes as vehicles of commerce, whether passenger/freight/mail or what have you. Some areas that could be of particular interest might be flights across or down the length of the Mediterranean Sea. Passenger/tourist service going from Turkey --- Spain could give some interesting possibilities, considering flying experience and familiarity with places that Germany would otherwise have only limited access to and information on in OTL. I would wonder what Greece could use for fast tourist trips to and from all those islands? Would the Italians possibly like some mail/passenger aircraft? Trying to make profits where ever they can, would force the Germans to make innovations and improvements if they hope to stay competitive and make a profit, and with all the experience operating floatplanes from their merchantmen, these programs, not at all of a military nature, could improve the German aircraft industries performance quite a bit, so that perhaps engines don't overheat quite as much, or fail as often/quickly for early military engines, and maybe, just maybe, the Germans learn earlier that engines will need replacing, and if one wants to keep a great many aircraft operational all the time, then the industry is going to have to up the supply of engines...
Amphibians:
So, back to giving the background for building a better --- maximum Kriegsmarine, we start getting away from entirely water based aircraft, and delve into the multi-tasking aircraft, that can still be competitive in markets that are beginning to have airfields in numbers sufficient to start shifting away from pure seaplanes, into a fleet of mixed land based planes and seaplanes. The construction of airfields is a foreseeable thing, and so the possibility of loosing out on market share can be hedged a bit by building Amphibians. Seaplanes like the H6K didn't really have landing gear, but rather had wheels that could be tacked on, and allow them to come on land. What if, some seaplanes had fully retractable landing gear, and thus could take off or land on either surface, regardless of waves/weather? Such a hybrid aircraft could have interesting possibilities for operations of a military nature later on, so...
Land Based:
One of the chief problems of the Kriegsmarine in OTL, was a fellow named Goring, so in any ATL where we are looking for a maximum KM, this guy either has to go entirely, or be severely reigned in, such that the KM will have the responsibility for security at all ports/harbors/naval bases and anchorages, and this means not just costal and AA artillery, but fighter/bomber/s&r forces dedicated to such facilities, that are trained in combat roles against land, sea and air attackers. With the peaceful use/requirement of merchantmen making full use of their floatplanes on every voyage, it would seem that the German ports would have a clear need to an integral/nearby airfield to handle the shoreside workload for these planes when their ships are in port, so construction of such would be done as needed, so by, say, 1935 or so, there would be such a network already constructed and up and running.
And of course...
Carrier Based:
Germany is denied carriers as per the ToV, and this is one of the most difficult and indeed crippling conditions enforced upon them. Unlike in the 1936 campaign in a game HoI2, Germany cannot just build carriers, from the mid 1930's on, and expect to really have anything like a fleet carrier force. So this seems like an unassailable restriction, that the Germans cannot get away with breaking, but is it really?
Many folks, I suspect, will not be willing to entertain the idea for a German carrier force, and for good reason, and even if the Germans build full on fleet carriers, starting in 1935, the best they can really expect is to have them in commission by 1939, and no real way for the Germans to have any time to attempt to develop any training and doctrine for their carrier air groups pre-war, and thus their force would clearly be the underdogs when going up against any UK/US carriers. For that reason, I won't mention them here other than as follows; For the KM to have carriers, and the carrier planes to operate off of them, and the pilots to gain operational experience from them, there simply is no substitute for being able to 'land on' a flight deck, and building a full blown naval aircraft carrier is not something that the Germans are going to be able to get away with in the 1920's {which is when the UK/US started getting their own programs up and running}, and so sans a partner, that has their own carrier force and is willing to lend a hand to the Germans to get carrier qualified and checked out, any carrier aviation the Germans may attempt is going to be lacking in experience. A non-military vessel, say something like a cargo ship built to transport small numbers of aircraft to, and even perhaps to fly/catapult them off when in range, far off places might be something to consider, and from there...
In general, I would seek a Germany that did one of a few things with all the 100,000's of lost worker years between 1919-1939, and some of these would be a national merchant ship construction program, a national 'green roof' plan {Where most every building in German gets a rooftop garden/greenhouse/chicken coup}, such that Germany may or may not be able to feed herself, but with thousands of constructed {
Artificial
Growing
Environments}, the needs for imported foods in wartime will be greatly reduced/eliminated, and a national workers training program. Having gardens/greenhouses means you need fertilizer, and this means nitrates, and if the French raise hell {and they will}, then the Germans can plead their case to world opinion, and say that their recent national memory of being starved mandates any government take any and all action to prevent such from happening again, and that these nitrates are needed to make the millions of tons of fertilizer that the 10,000's of AGE's need to produce crops.
On the financial side of things, I would find ways to {encourage} the wealthy to sponsor privately funded initiatives to keep Germany working, and striving for zero unemployment instead of what they had in OTL.
Gosh, I'm tired and sleepy! Hope at least some folks read this and come up with some ideas, and ready to read everyone else's ideas for a maximum Kriegsmarine.