Best filetypes you will find on Limewire are avi and mkv. But don't let just the extension guide you, as an e.g avi is just a container (Audio Video Interleave) can be lots of things (DivX, XviD etc.) and same goes for sound in the file, which could be anything from low quality mp3 to untouched 6 channel AC3. Same goes for MKV, which is normally h.264 codec with either AC3 or ACC sound.

Other could be MP4, which also contain e.g. h.264 video codec and ACC sound.