OK, after trying a bunch of weapons on my Soldier run I'll go with this list (might change when I try other weapons out)
Assault Rifles
Lancer - good damage, no ammo problem, decent accuracy, slow reload
Particle Rifle - decent damage, no ammo problem, good accuracy, slow reload
Avenger - low damage, ammo problem (not much though), good accuracy, fast reload
So far my favorite is, surprisingly, the Avenger. When you mod and upgrade it accordingly and mix with some weapon damage armor it is quite a decent weapon. Doesn't do sh*t on boss-type enemies but I use powers on them anyway. It kinda fits my playstyle the best. Lancer didn't make it because I never manage to stop shooting at the right time! 
Sniper Rifles
Mantis - great damage, slow reload (mitigated by canceling), decent ammo capacity
Viper (with Marksman RoF evolutions) - ME2 Viper, decent damage, fast reload, good ammo capacity
I'm more of a one shot-one kill type player so it's Mantis for me.
Heavy Pistols
Suppressor - great damage (headshots are insanely good), good accuracy, decent ammo capacity
Scorpion - good damage, low ammo capacity, decent accuracy, collateral damage, works great with Cryo Ammo
Suppressor. And not because I love stealth genre, the gun made me double check difficulty when fighting Spectre-level opponents on Insanity
SMGs
Locust - good damage, great ammo capacity, good accuracy, fast reload
Love how you can just shoot it without aiming and hope it hits something. Tempest has that ability too but slow reload kills it for me
Shotguns
Graal Spike Thrower - multiple shots, great damage, decent ammo capacity, good accuracy
Never was a fan of shotguns but when krogans make something to hunt Thresher Maws, it's good 