So this is going to be hooking up to your computer?
I just want to make sure about what sort of speakers/subwoofer you need.
Is this just a personal system for when you are laying down your mixes? Or are you trying to find something that you can actually use for performances?
$50 is a SERIOUSLY low budget for speakers. I'm not trying to sound like a jerk or something, but just to be very honest, it's not really possible to make and sell a good subwoofer for that sort of price. You would be better off with a pair of monitors, which is what most pro or semi-pro mixers use for music anyway. Very few mixers use a subwoofer. Obviously, if you're performing at a club or something, you'd be hooked into their sound system with huge speakers and subs. But just for laying down your tracks at home, I wouldn't recommend looking for a subwoofer - especially with such a low budget.
To be honest, your best option would probably be a pair of decent headphones. But obviously, only you could hear if you're using headphones. So again, I don't know if this is just for personal use, or if you want something that other people can listen to as well.
You can get some half-way decent monitors like these
Behringer MS16 for a hair over $50 . Most of the time though, you'd be looking at about $100 for a solid, entry-level pair of studio monitors. For headphones, you should be able to find a decent set of Sennheiser, Shure or Sony cans that'll do the trick for you.
Best of luck!