An accurate domed pellet is best overall, IMO. Some situations might require a wadcutter or a hollow point on light bodied critters (Hosp's, chippers, etc.), but accuracy takes priority. If (and a big IF at that) you're guns shoot Crosman Destroyers well, they hit very hard and open easily. Unfortunately not many guns shoot them with enough accuracy.
As for specific pellets used, I've used H&N FTT's & Baracuda Hunters, JSB/Air Arms domes, various Crosman domes & hollow points and Daisy/Winchester (new style) Hollow Points with good success in .177 & .22 for most of the pellets listed. Some bigger critters might need a harder pellet, so I'd go with a Crosman or (maybe) H&N domed to get through tougher/thicker skulls, JSB/A.A. and Daisy/Winchester pellets are very soft and I'm not sure they're up to the task.