Recording is a pretty wide field, and much of it depends on what you want to achieve and what kind of music you want to record.
I mainly record acoustic music, string quartets, folk ensembles etc. As such I have built a computer based recording set up round based on my needs of only recording upto 2 inputs (mics or line level) at a time. I know that other people on this forum use hard-disc based recorders however.
So the main things you need to decide before you embark on the mamouth journey that is recording, and before we can give you any worthwhile advice is what you want to record, and what you want to achieve.
Firstly how portable do you want your kit to be? If you only intend to record yourself, or other musicians one at a time in your own room, then a computer based set up is worth lookign at. If you want to do a lot of location recording and be mobile, then either a lap top, or preferably a standalone harddisc recorder would probably be the best option.
Once you've decided on this then affects the next steps. If you want to record a full band, and use a computer based DAW (digital audio workstation) then you'll need an audio interface with plenty of inputs, so firewise units will be the best way to go. Always pay for the best AD/A convertors you can afford, as these will have a massive bearing on the soundquality. I use an Emu 1212M soundcard which has nice convertors, others here also use Emu soundcards.
A popular alternative amongst some is to use a harddisc recorder to capture the sounds, then use a DAW such as Cubase, sonar etc to edit and process the sounds in a computer.
I could go on, but really to best focuss my advice it'd hgelp to know what you want to record and where :)
Hope that starts you off in the right direction tho.
*Rahnooo*