You'll need a soundcard, so you can split the channels and play Track A out loud in the room, and Track B in your headphones for mixing, for example. You can get them pretty cheaply tho, if you look around. My first one was a Creative Soundblaster, which cost me about £35, but you can find cheaper ones than that.

If the soundcard eats too much into your budget, then you could possibly look into this mixer instead:

Hercules DJ Control MP3 E2 USB DJ Controller with Software - DJ Equipment from Djkit.com=

I haven't used it myself but I saw it at a house party a while back and it seemed like it'd be good for a starter mixer, to learn on. It comes with Virtual DJ, but Numark Cue which I mentioned above is basically a branded version of the same program. It is literally a basic, started mixer, but you got to start somewhere and there's no point splashing out £1000 on a mixer, only to find that you don't really like mixing after all!