Yes, I think you are on the right track with EAC.  If you want lossless compression, the most popular format is FLAC or Monkey's, but you'll want to make sure whatever you are going to play the audio on supports decoding whatever format you choose to encode in.  My experience is that mp3 and wmv is support by all players (except Apple products) but they are lossy.  Fewer players support lossless formats like FLAC.