I usually use the Devidian gun and the TOS rifle when I'm soloing. Got into Infected and The Cure this weekend for the first time in a long time with my ENG and used the Breen Ice Maker pretty much all of both runs. It was nice because it's one (if not the only) weapon whose number #1 attack is an expose on top of the usual #2. I thought it was nice that way. The special attack takes a little getting used to. It's a good opener or mid-fight ability because if you wait much longer, the mob you're targeting could be dead by the time it fires. Just takes some getting used to.
My main primarily uses both the Proton rifle and a high-end sniper rifle and I switch back and forth to mitigate cooldowns and take advantage of exposes as they happen. (And I make sure my BO's have good expose weapons!) I like the chained lightning effect of the Proton rifle. However, the Proton Rifle exploit shot does take a couple of seconds to complete and do the full damage. Rate of fire is overall slower than even a sniper rifle, or so it seems to me. As a Science officer, I probably would not use the Proton rifle in PvP.
The Cryo rifle stays in the hands of my Breen Tac officer, who is always on the ground with me. He's one of the reasons I get so many chances to use an exploit shot. I might borrow it if I get around to doing any PvP, though.
One weapon I really, really liked using was the Rare Overcharged Plasma Sniper Rifle. Damage output is fantastic at the rank you get it at (Captain, I think?) and holds up well even into higher ranks. I forget which mission offers it as a reward.