Monkey's audio is considered to be the most efficient compressor. Drawback: windows-only. FLAC is open-source, and seems to be popular on this forum, so methinks its success will be a fact

This is the core. I'd like to add that Monkey's 'highest' setting is far more CPU-intensive than the 'high' setting (not only for compressing, but also for playback later on), whereas the compression is hardly better. So 'high' is probably what you want (unless you want to transfer files over the internet, but that's not very likely...).
Optimfrog is another lossless compressor that compresses very well too.
There are nice tests (comparisons between all compressors), although I don't have any links ready atm (I am one of the lossy guys. 'Lossy' as referring to the kind of codecs, rather than someone who loses everything

). I am sure someone else here will have the links
What is streaming? Streaming is what internet-radio does: instead of first transferring a file (mp3) over the internet and only when finished starting to play it, streaming means you listen to the music while the rest of the song is still being transferred to your computer: by the time a few bytes (= a certain part of the song) arrive on your pc, it is time to to play those bytes (= that part), and whilst they are being played, the next few bytes are on their way... So you listen to what comes in.
(I guess the no-stream issue is not important for the time being as internet transfer speeds are limited, and will remain so for quite some time)