Considering that Germans now has Mittelafrika and the East Indies, they need more rugged small arms. The Gemans will likely develop SMGs based on the PPSh-41. As for Assault Rifles, the evolutions of the Sturmgewehr will likely be (more) similar to the AK-47/74, due to the need for reliability in harsher environments. an M14 analogue may be developed as the new semi-automatic battle rifle, but it's more likely that the STG-47 (thats what I'll call it

) will be adopted as standard issue by the German Armed Forces.
With artillery, rockets will likely become more important than tube artillery, and whatever the Germans make will likely be a Nebelwerfer-Katyusha hybrid.
As far as the Navy goes, the Germans won't develop submarines as much as they did, aside from SSNs. This is because they are going to focus on force projection, which is the job of large surface fleets. Due to Nazi egomania, they'll likely build some useless battleships, but they'll also build some aircraft carriers, which actually have value.
In the air, the Germans will develop further their jets. I don't know whether the Germans focused on speed, maneuverability or firepower, so aviation experts could answer better than me on this. The Germans did have plans for the 'Amerikabomber' which was an inter-continental strategic bomber. If they planned to fight the US, or were in a Cold War with the US, they would also need advanced Naval Bombers.
For WMDs, I imagine the Germans would develop biological and chemical weapons, largely for clearing troublesome populations in the new colonies. One very interesting thing about the Nazis is that, despite the fact that many of the projects were funding sinkholes, they were very imaginative. There will definitely be Nazi ICBMs, and a Trans-Atlantic Cold War will focus on ICBMs, rather than tactical nukes or SRBMs.
The Germans will probably give up their mega-tank designs, but will continue experimenting with flying saucers, and possibly even Tesla-style energy coil weapons.