I'll admit that I'm still in the fairly early game (about 3-4 months in on hard) so I haven't reasearched a lot. But the heavy weapons seem to have it for me. I haven't actually been worried in the game so far and am starting to wonder if the whole research thing isn't a waste of time for everything but armour, craft weapons and better craft. I tend to out-sniper the enemy every battle, with just enough stuff in reserve for close-quarters if I need it.
#1 Rocket launcher. Good: Long range, good accuracy, splash damage (possible indirect kills), cheap TU cost, highish damage.
Bad: One shot, expensive ammo, civilian casualties.
I carry 5-6 of these as a main weapon in my squad with a reload in the holster. Fire, forget, drop and pull out your "actual" main weapon from your backpack. Makes you feel all evil and commie but by god does it work. 10-12 rockets flying everywhere in 2 rounds finishes almost all opposition (and sometimes a poorly informed civilian).
2: Sniper rifle. Good: Accuracy(ducked), shoot through walls, 5 round clip, alright power, can still medi-kit someone without dropping it.
Bad: high TU cost for accuracy, needs ducking, sometimes woefully inaccurate.
Sort of like my backup rocket launchers. 2 as main weapons, 1-3 in backpacks with a spare clip. Sniper team at a moments notice.
3: Machine Pistol. Good: Fits on your belt, good ammo, low TU/shots output, makes all soldiers multi-purpose/close/medic experts. Bad: crappy damage, low ranged accuracy, hopeless vs heavy armour.
It fits on your belt. What else is there to say? It also fires 8 shots for not many TU with suprising crouched accuracy. Just something to pull out and spray at whatever you want/can't hit any other way. Ultimate secondary weapon.
My other favourites are the MG and the grenade launcher. I'm actually leaning toward's the MG instead of as many snipers, the "1" shot kill of full auto is amazing, although they make my squads a little too static for my liking. I like grenade launchers (and grenades) for the very cool things you can do with them. Can't quite reach an alien? Target 2-3 Z-levels up (by holding shift and pulling back a square or two), timed burst and pretend your mini-artillery. Works more often than not....
My standard soldier (pretty much everyone) has armour+night vision, a RL or sniper equpped, medikit+rocket/magazine in holster, machine pistol+grenade on belt, and then either a sniper/MG/GL+clips+grenades in their Backpack. or just a random weapon I want to try. Nothing has ever suprised me, and my poor troops carry this enormous load without a hitch. Even the bugged "big-city" wasn't a problem with a loadout like this. Eveyone can do everything, with enough ammo to keep on going regardless. Plasma smasma