A bit a tough call for me, to be honest. Still, here's some of my favourites:
Black Widow -- The one thing that I don't like about the Widow and Mantis is that they're single-shot clips; I just don't like it when I have to reload after every single shot. The Black Widow has the power of those rifles (well, slightly less), but a three-shot clip. Perfect! I actually ended up using it for about half of my first playthrough; in other words, almost exclusively once I had bought it. The only downsides to this weapon is the heavy weight and small base mmo count; the former you just have to deal with, the latter can be fixed with the spare ammo mod (sometimes another mod would be nice) and an ammo power bonus (lose the headshot bonus). Nevertheless, this weapon makes mince-meat out of the toughest foes in the game; armored foes, once that armor is weakened with warp or other debuffs, can be killed in a single clip.
Mattock -- My go-to weapon in ME2, and much the same in ME3. Semi-auto nature rewards precision, but rate of fire and clip-size allow for some spamming (just have to keep you aim on your target). Not too heavy either.
Sabre -- The Mattock with significantly more power, it's almost a sniper-rifle. I actually ended up attaching a scope to it, and it helped a lot with the aiming of this beast. You don't really need the scope for the extra accuracy it gives the weapon; but it between the slow rate of fire (no spamming with this gun) and recoil, it definitely helps the player aim better with it. Weight is an issue you just learn to deal with, but the small clip size (for an assault rifle) can either be worked around or fixed with a mod. Also a tad slow to reload as well, but not too bad (Revenant is awful for that).
Graal Spike Thrower -- Scarily accurate shotgun. Like the Sabre and Black Widow, the main issues are the weight (yeah, I pretty much learned how to live with -200% power recharge times). The surprisingly good accuracy of this weapon means it's actually easy to miss, and the fact you can charge your shots gives you all the more reason to aim well; you can use the accuracy mod to reduce the spread of this weapon, making it useful even at longer ranges. Nevertheless, a charged shot from this thing (and when all the spikes hit the same target, which they usually do) obliterates it. The only concern is the ammo: three shot clip, not much in reserve (fixable with a mod), and a bit slow to reload. You really have to make your shots count.
Disciple -- I'm not a huge fan of weapons with a lot of spread, but this was the shotgun I used when I felt like I needed something like that. Shots got a nice sci-fi sound to them, and it works well.
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I didn't use many SMGs or Pistols during my first playthrough, so no comment on those.
But if I had to pick a single weapon as my overall favourite?
Black Widow
The power of a single-shot rifle, but with a three-shot clip.
Every bit as awesome as it sounds.
