Hi, all. I had an account here many years ago, but lost my password and got rid of the associated email account, so I've only lurked for about a decade. Frankly, I don't know enough history to contribute- at least to this board's standards, which seem pretty demanding. But on this topic I can, so I re-registered.
I'll get to other points later (this will be long-winded) but the OP asked:
If you could equip American forces (using our current mission requirements) what infantry rifle would you use?
First, the AK is not going to cut it. It's legendary reliability is overstated. It is woefully inaccurate. It is heavy. It is criminally unergonomic. It isn't a horrible choice for many militaries- it is cheap and available- but it is horrible for the US military, for the many reasons others have stated above.
[Anyone who spends any time immersed in "gun culture" will swiftly realize that there are immense amounts of fanboyism, hyperbole, posturing, and sheer rank idiocy involved. So be skeptical of anything you see on the interwebs about guns. Including this.]
Second, no Western nation will ever ever have a 7.62x51mm battle rifle again. The few that retain them will eventually replace them, and never have one again. Both the weapon and the ammunition are simply too heavy. Sticking to current real-world conditions, I agree with others, that sticking with the M16 family likely is the best option. But which one? Though it hasn't been in use long enough to be definitive, the HK416 is looking like it is going to prove to be an excellent weapon, and I think I would favor it.
The logistical argument is obvious- we already use M16s and are familiar with them. It's also possibly the most ergonomic combat rifle ever made. I see an awful lot of Britons, Germans, Danes, Norwegians, etc. all walking around with various models of M16 on my deployments- usually the special ops guys- despite having their own indigenous rifles available. Clearly, the merits of the M16 are recognized. And it really doesn't need significantly more TLC than any other Western rifle, all of which tend to be made to closer tolerances than the ubiquitous AK.
5.56mm has a great virtue in being light and light-recoiling, which makes it easy to carry a lot of it and simplifies training. It is far far better to miss a target 100 times while hitting it once with a 5.56mm, as opposed to missing it 40 times and hit it zero with a 7.62x51mm. If your answer to the hit ratios is "well, that's a training issue" I would respond "no, it's a reality issue." It is not realistic to expect to train every 18-year-old recruit who barely passed his ASVAB to special operations standards. Not to mention that there exists such a thing as suppressive fire and fire superiority, that it does matter, and that having more ammo helps achieve it. Further, though I am in the Army, I agree with the USMC's move back to a full 20-inch barrel as their standard. The most lethal 5.56mm we have ever had was the initial 55-grain projectile screaming out of a 20-inch barrel. It would reliably fragment and produce impressive wounding even at comparatively long ranges. Armor penetration suffered, but it was indeed lethal. The 14.5-inch barrel should really just be used as a PDW or something. Heck, a 10-inch barrel would work as a last-ditch PDW.
[On the other hand, the USMC is barking mad for eliminating the SAW gunner in favor of an "automatic rifleman." That has been tried many times before and has an unmitigated record of failure. But I guess there are just some lessons that we have to re-learn every now and again.]
Back on topic: Most of the complaints about lower wounding with the shorter 14.5-inch barrels is hyperbole... but some isn't. The issue M855 rounds only fragmented out to 100 yards or so out of the shorter barrel, and that unreliably. However, the new M855A1 round has largely fixed that and also has great penetration. In fact, some have called it semi-armor-piercing. Win, there.
The high (though pretty much unplanned) modularity of the M16 platform is another bonus. We could issue two uppers- one 14.5-inch and one 20-inch, to be used depending upon mission requirements. There does appear to be a need for longer engagement capabilities in some regions of the world where they come into play. A 20-inch barrel solves most of this. The rest could be solved with a third upper in something like the 6.5mm Grendel, if we really needed it in a battle rifle. That would require a lot more development before it could be issued, though, as all of those alternate AR calibers are still immature. (The 6.8SPC is a bit of a pointless dead end, now that we have the M855A1 rounds. It's external ballistics are actually quite pathetic, since it was designed for high energy delivery to short-ranged targets, whereas external ballistics was almost the entire design goal of the 6.5mm Grendel.)
Bullpups. I agree with others that though bullpups have their advantages- primarily being retaining long barrel lengths in a short overall weapon- they are probably overstated. If nothing else, firing around a corner in an urban scenario using your off-hand is very... uncomfortable. Specifically, the hot brass tries to implant in your face. Stepping out from behind cover to fire with your good hand is worse. The only work around for this is either caseless rounds or a complex forward ejection system. Or, of course, novel magazine mounting such as with the the P90 or the old G11, which are very awkward to reload quickly. Being able to reload any bullpup quickly takes a LOT of training, especially if you don't want to take it down off of your shoulder so that you can put your one chambered round into a Bad Guy who might suddenly appear. Clearly, many respectable militaries use them and like them, so I'm sure that they are a viable option. But if you want my opinion- and opinion it is- I would stick with a conventional layout. The options that give the M16 a challenge- again, IMHO- are other conventional-layout designs like the G36 or FN SCAR. The SCAR isn't proven enough to my liking yet, though. But it would certainly be ergonomically compatible with M16-trained troops, and I think it has potential.
OTOH if the OP meant to ask "What is is the bestest most awesomest Western battle rifle on an individual level as opposed to an issue level?" then that's a different conversation. But as asked the list of contenders has to include M16 (HK416), G36, and FN SCAR.
On to off-topic stuff that has come up...
The LSAT program. Current advances in small arms are largely material, not basic design. (Polymer chassis such as the G36 or FN SCAR come to mind.) It will be difficult to improve upon current designs, the M16 included. The LSAT program has some promise, though- I just don't think that future developments are what the OP had in mind. Personally I'm a 6.5mm fanboy, but I think sticking with something around 5.56mm is probably still the way to go for an issue battle rifle (unless they can get the weight of the 6.5mm down considerably). People like the 6.5mm because of it's awesome ballistic coefficient, as do I. But 6.5mm projectiles have that awesome BC solely for historical reasons! To whit: the projectiles are very long and heavy in proportion to their their caliber compared to most others. Since we're starting from scratch with the cased telescoping (or caseless) rounds of the LSAT program we should be redesigning the 5.56mm projectile to be much longer-for-it's-caliber, too. Then it would likely be capable of meeting the long-range engagement requirements by itself, with a similarly awesome BC. Back when the M16 first came out the long-range service rifle shooters all poo-pooed them... until they started winning all of service-rifle matches. The 5.56mm, properly loaded, has better external ballistics than any realistic 7.62mmx51 loads. Nowadays you never see anything but M16s (actually, ARs) in the service-rifle matches. For a reason. Terminal ballistics, yes, are not as good at extreme ranges. But a longer projectile (that would have a very rearward center of gravity and tumble easily) would fix that, too.
Handguns. Any time someone uses the term "stopping power" in relation to handguns and it isn't in scare quotes, you should probably ignore everything they say. (Yes I exaggerate for humor- I hope my point is understood, though.) Joules is not "stopping power." Muzzle energy is not "stopping power." The truth is, we have no idea what "stopping power" is. The only remotely scientific data anyone has ever gathered defined it as "the assailant ceasing aggressive action," which more often that not means a psychological affect, not a physiological one. So this is very hard to study. That data also shows that above a certain minimum (probably somewhere between .380ACP and 9mmP) that caliber doesn't matter. The only independent factor that matters is how many times you hit the guy. Handgun rounds are low-velocity, enough so that temporary cavities do not really come into play. (Unlike rifle rounds, generally. Don't get me started on Fackler.) So handguns all just poke holes in things, and the statistical difference between a 9mm hole and an 11.4mm hole is trivial. That wound channel has to intersect a vital structure. (And if you really want to get persnickety about caliber then two 9mm channels are superior to one 11.4mm channel.) I personally don't like 10mm rounds for logistical reasons. The .40S&W has proven to be overpowered for every platform we've tried to use it in, to the point of cracking slides over long use. Probably because most have been based on prior 9mm designs. A decent reliable gun could probably be built around it, but none has to date. (Though I admit I haven't paid attention for a few years, so I may be wrong.) Also, the entire thought process that lead to it was flawed- the FBI drew entirely the wrong conclusions from the Miami Shootout, as they themselves have recently tacitly admitted. Modern +P 9mm is at least equivalent to .40S&W.
Every other handgun stopping power study or metric has either been fatally flawed or obviously biased (usually by the .45ACP fanboys, of whom I am one, so that should tell you something).
So within those minimal limits an easily-controllable, more-easily trained, and higher-capacity caliber would be assumed to be superior. So we're talking about 9mmP or somesuch, here. Any of the current polymer "wondernines" would serve. Glocks are good, and widespread, so they have a logistical benefit. I personally am not a striker-fired guy, but I could learn. I like SIGs, and they would be a great choice if you don't like polymer wondernines. I love shooting my 1911, but proposing that a 100-year-old design would be a quality combat handgun by modern standards is madness. They are incredibly maintenance-intensive, low-capacity, and unreliable. Some groups like LAPD SWAT and USMC are trying to use them again as they re-learn whether or not there is really a benefit to .45. [As I said, some lessons just need to be re-learned.]
The Beretta M9 is a monstrosity. An exposed barrel (to both burn your hand and allow crud into the action) and a slide-mounted safety (that you can't reach)? What the hell were they thinking? A combat handgun shouldn't have a safety! In the unlikely event that you need a handgun then in all likelihood you will need it very badly, and very quickly. So no safety- at best a decocker on a double-action capable gun, or none at all like a Glock or the other striker-fired guns. I understand the US military's concern about not having a positive safety, but a decocked double-action would be very reasonable.
Similarly, don't listen to anyone who claims that shooting a human with a 12.7mm projectile is a violation of the Geneva Convention. That's a longstanding myth that Just Won't Die. Distressingly, it is even perpetuated within the US military by ignorant NCOs who read it on the internet once, or something. [If you are one of them, for the sake of your troops I urge you to request a Geneva Conventions briefing from JAG and ask them.] Many nations are using .50 caliber sniper rifles, for instance, and there are no Danish reporters having fits about it.
Whew! Sorry, that was a lot. In particular, I find myself dispelling "stopping power" fairly often. But I have to stop. I have a case starting. So I also haven't had a chance to do my usual re-editing to avoid ruffling feathers- I apologize if I offend anyone with my gruffness. People tend to get very prickly about this topic.