I've tried to pick only one per CTU per side, so you don't have to spend as much renown.
Attackers:
Thermite - basically a requirement for any attacking team in every patch of the game. No-one else can get through reinforced walls. And they turn up a lot.
Twitch - bit more of a personal one, but her FAMAS is probably the best gun in the game and her ability is extremely versatile in both clearing rooms of gadgets and doing minor damage/finishing off enemies. I personally prefer her heavily to Thatcher.
IQ - I've always been of the opinion that she's been good, thanks to her great guns and speed, but in the new patch she's excellent, thanks to a decent buff to her ability. She also murders Pulse outright (I have basically made matches instantly 5v4 with her shooting a Pulse from miles away through a wall), and hard-counters Valkyrie's cameras, which are otherwise extremely good.
Fuze - Not as powerful as he seems, can be a noob trap, and is counterable, but no other operator has the sheer killing potential that he has. Very good on secure area missions in particular. Don't pick on hostage unless you are certain you are not going to kill the hostage.
Defenders:
Bandit - stops thermite, at least to a point. You can usually effectively cover off at least one whole wall of a room with bandit, which makes him very good, and what makes twitch and thatcher's abilities good. Mute can also do it, but he doesn't destroy the charges, only stops them working, which isn't nearly as good.
Rook - His ability is good in every situation imaginable, being able to effectively take about one more bullet with a much greater chance of not being instakilled. In every round he will make a difference.
Smoke - if nothing else, being able to deny entry to an area for a certain amount of time is just great on defense, but his killing potential is ridiculous, especially against shields.
Tachanka - Tachanka isn't good. Unfortunately, out of the ones i've suggested, i'm only left with the awful FBI defenders (Pulse is too easy to hard counter in my opinion, Castle is a downright liability) and the Spetznaz ones. Kapkan is awful, and basically adds nothing to your team because his traps do pretty much nothing against anyone with more than half an hour in the game. Tachanka at the very least has an ability which can turn the tide of battle and he's great at setting up ambushes where the enemies don't expect. He's also by far the most fun DEF operator in my opinion, though Valkyrie is also - though costs up to 50 times the amount.