Are you looking to just record some demos, or really learn recording and come out with fully completed tracks? Either way, you'll need an interface, something simple like
this should work great for home recording, it'll give you the option of either plugging in direct and using amp sims, or plugging in a mic and miking your cab (as well as using that mic for vocals and other things as needed). Then you'll need a decent set of headphones (especially if you're recording with a microphone, direct stuff can be done through speakers) and/or speakers. As far as headphones go, anything in the "pro" line from AKG/Sennheiser/Shure/Sony/similar in the $50+ range should be a good start, though the stuff at around the $150-200 mark is awesome. I'm less up on speakers these days and what's good, but listen to everything you can and pick what you like the sound of.