There are many (interesting) discussions about this subject. On one thing we all agree. Lossless codecs are better in terms of quality, but a lot bigger compared to lossy codecs. Some people hate the quality of MP3 and some don't hear the difference between MP3 and a lossless codec as FLAC.
Between lossy codecs there can be a big difference between quality. Between lossless codecs this is not the case. Lossless codecs work like RAR and ZIP archives. You can compress and decompress without loosing any data. No details or frequencies are lost during this process.
Lossy codecs work differently. They write a 'summary' of the music. They save the important, most audible, data only. The rest is lost during the compression. This means that some (higher) frequencies and details are lost.
If you understand the descriptions above you should understand that you can transcode FLAC to Apple Lossless without losing any quality.
On the other side you WILL LOSE QUALITY if you encode a lossy file to another lossy file. The encoding will 'write a summary of a summery'. This is considered 'illegal' in audio world. Don't do this if you can avoid it! Even when you recode a 128kbps MP3 to a 320kbps MP3 you will loose quality! It will sound worse and will be bigger as well!
That is why MP3 files are always created from lossless sources

2. Most used Audio formats
Lossy
MP3
AAC / M4A (also used by iTunes)
WMA
Ogg Vorbis
AC3
DTS
Lossless
WAV (PCM)
FLAC
Apple Lossless (also named M4A)
SHN
Monkey's Audio
WavPack
3. Playback software
Windows Media Player
Supports MP3, WMA and WAV out of the box. For other files you'll need additional DirectShow filters like FFDSHOW. Playback is then possible, but the integration of these files into the library is not good at all.
Foobar 2000
The most customizable player which is also free. Supports a lot of handy technologies like ReplayGain (automaticly amplifies quiet tracks). Good tagging and good library. Supports every audio codec on the list above with additional (free) plugins
Out of the box very powerful. Must have for powerusers. Tagging, encoding, renaming is very easy if you have done it once or twice.
Winamp
Easy to use, supports a lot of formats. Has loads of plugins and a good library. A bit slow, but an excellent choice for WMP users who want a bit more. Be careful when installing this player, it is bundled with 3rd party software.
iTunes
I don't know much about this one. The times i have tried the player it was really slow. I heard that on a Mac it is a lot faster. Very easy to use. But not as extensible as Winamp or Foobar 2000.
4. Common 'problems'
A lot of problems are also in the source. Please check if a new source is available.