Expose/exploit is kind of a wasted mechanic these days. Most enemies don't have the health, so by the time you can set up an expose and then hit them with an exploit, they're already dead.
Boffs pretty much suck with exploit weapons, though - they don't use their offensive abilities very intelligently, just whenever it comes up in their action priorities and on whatever they have targeted. But since it doesn't really matter, high DPS weapons are usually best.
Miniguns are probably one of the best weapons in the game for boffs, huge DPS, high rate of fire, AOE, until you get to fighting Borg, where they'll adapt quickly because of the high rate of fire. Pulsewaves are especially good against Borg and usually good all around anyway.
I found that my boffs manage quite well with weapons I got from episodes. One purple polaron pulseweave assault rifle from cardassian episode, two disruptor split beam rifles from romulan episode and one CRM200. They don't have problems with borg missions or any other episode. I'll probably give all of them jem hadar sets once weapons become non-unique.
My team is heavy on grenades, so two pulseaweaves (one mine and one boff) are very handy. 2 or 3 grenades and two secondary shots from pulseweaves will kill all ensign level mobs and heavily damage lt. ones.
Well, I've been farming elite STFs, and I have way too many proto borg salvage. My ship has full Mk XII, and I'm doing Skirmish again and again to rack up Devidian kills for the accolade, providing a ton of XI personnel shields...so now I'm just kitting out my crew in Mk XII antiproton weapons.
I've been pretty much just choosing them at random or based on RP considerations (giving my Orion dual pistols, etc). I've just been wondering if a particular type is better than another or if just going down the list and handing out the weaps at random is fine.
For brute force a whole squad full of assault miniguns can be rather entertaining especially with full auto and flanking the enemy from multiple directions.
But, logically you will need to have some weapons do expose damage (like a MG) and other weapons (snipers) to do exploit attacks once the enemy is exposed.
I also have at least 1 engineer and 1 science boff for construction and light medic duty. Tactical is great for grenades but the lunge attack, not so good in a pitched battle because she will tend to rush forward too soon.
Pistols aren't so good because the boff will tend to close with the enemy too fast, rifle range is always best.