I've used EAC to do this. Instead of ripping individual tracks, tell it you want to "Copy Image & CUE Sheet." That will make a single WAV file of the entire CD, then you can convert to MP3 from that.
Just because your MP3 player doesn't support AAC -- the format used by Apple's iTunes Store -- doesn't mean you can't still play those files. It's simply a case of converting the files from AAC to MP3 ...