First, lets clarify the basics: Lossless data compression is a class of data compression algorithms that allows the exact original data to be reconstructed from the compressed data. The term lossless is in contrast to lossy data compression, which only allows an approximation of the original data to be reconstructed, in exchange for better compression rates.
Lossless compression is used in cases where it is important that the original and the decompressed data be identical, or where deviations from the original data could be deleterious.
- MP3 and AAC (=the fruit company) are lossy compression.
- FLAC and APE are generally used loseless formats.
Be aware, that some cheapest media players and also mobile phones cant play these formats. APE is supported by only few media players, so be aware!
Usually FLAC-s are ripped from CD-s at 12bit/44kHz resolution. Some FLAC-s are HD audio capable 24bit 48 kHz, 96 kHz or even higher definition. This is also too much for some players.
AIFF is widely used uncompressed high-quality sound format widely used in Apple world, but is not supported in any media player I know and had.
Last, but not least - good (= high bit rate) MP3 is generally more than enough for enthusiastic listening. High bitrate means generally 160, 192 or 320 kbps.
My recommendation: If You are leaning towards to audiophile listening and are enthusiastic to play studio master quality stuff, choose Your media player (or transport / DAC) wisely. It should support APE, FLAC and at least 24/96 D/A conversion.