that's a tough question to answer because it depends on whether you wanna record amateurly or professionaly or just for the sake of screwing around... it also depends what kind of computer and recording setting you have.
my best advice because when i was strictly in my bedroom and didnt have a studio and wasnt trying to record stuff i did the following:
my suggestion is get like a pc based DAW or if you have an apple then apple based. you can get like "light" versions of pro tools, sonar, cakewalk whatever and get a usb or firewire based recording console like an mbox which is prob the best in its class and get a very good (and industry standard) recording mic like the sm57 which is cheap ($90-$100) and you can record like that. if you are not recording to mix and make full songs and stuff you can't go wrong and having things like the mbox and the experience you get from playing around with computer based digital recording programs will help you out if you want to get better or more involved in recording stuff and writing songs.
otherwise you can get like a 4-8 track one of those like fostex or boss or roland all in one workstations and all you would need is a mic. you can actually mix everything there and make mp3s once you bring into your computer via USB or FIREWIRE. the advantage i see for the computer based is that it is a gateway and an easier transition into the world of recording because you have hands on learning and experience with computer workstations..... the all in one route will probably be cheaper but you will have to upgrade anyway if you want to get past bedroom recordings.