For assault rifles (maybe pistols and SMG's too) - FMJ (standard), AP and Incideary...HEAP?
I generally assume the standard bulles are already AP. It's not like the aliens spend much time armourless and that stuff is rather annoying to get through.
Maybe advances in nanotech and alien materials could allow you to produce better armour piercing bullets?
Because I don't think we really know exactly how heavy those things are other than "heavier than the stuff we use on our own aircaft" so it might be just using the stuff on the jacket would be a better idea.
For the bazooka a plasma missile or a sabot missile...HEAP?
Plasma should work and it's already in the grenade launcher and while I'm not really sure how effective sabot rounds are with rockets and recoliess rifles*, I always assumed the launcher had HEAT anyway. Thermobaric, maybe?
*The launcher is based on the Carl Gustav, right?HEAP rounds for Shiva cannon.
If the Shiva and the sniper rifle still share their calibre, they could be given some sort of small plasma based explosive as a research as well as the previously mentioned alien AP.
Come to think of it, it'd be nice if earlier weapons could be updated with later advances.
The research message from the needler already mentions the benefits of reproducing its holographic aiming system for other weapons.