Drums are always the hardest instrument to record and usually the most expensive. For your budget it sounds like you might have to make a few compromises.
Personally I just use Logic Express on my Macbook Pro with a Tascam US-144 interface and a SM57. It has two mic/line inputs, which doesn't give you a lot of options for drums necessarily. But for a young person just getting into recording, you really just need to keep it simple. Getting a couple of condensors or a condensor and a SM57 would be a usable rig. As tough as drums are to record, having to mix 4-6 microphones can be too much work for someone who has no idea how to do it.
A good friend of mine that plays drums (along with a host of other things) introduced me to ProTools a few years ago. He had a pretty simple setup at first, but it yielded usable results. He got a kit of Audix budget level drum mics and ran them through a mixer into his interface. It was basically three tom/snare mics, two overheads, and a kick drum mic. I don't know how much it cost him, but that may be something to look for. It was nothing special but it got the job done.
Everyone records their own way, and there are definitely no steadfast rules. I've heard what should be a good drum track sound terrible and a cheaply recorded drum track sound pretty good. In the end, try to find an interface that let's you expand your setup later on if you want to keep going that way while in the present you provide a decent, if minimalist, rig.
