Say I roll two hits and a crit and my opponent rolls two evades and a blank. Does he choose which dice to cancel out?

Cancel out all regular hits first, then cancel out any critical hits.

So if you take 2 regular hits and 2 critical hits, and you can prevent 3 damage, you'll end up with 1 critical hit.

Super LoFi said:

The "regular" hits are resolved first; then any critical hit left. The defender evaded the "regular", but the crit (face-up card) went through.