I agree with all that's been said here. I played on crappy cymbals for way too long. When I was a teenager, I was able to make my crappy drum set sound pretty darn good with precise tuning and good heads. But you can't do anything about the sound of cheap cymbals.
However, I will say that what's "cheap" nowadays is far better than the crap they were slinging 20 years ago. I have a couple Paiste PST 7 crashes that sound great.
Just an FYI: I think the best budget snare drums are piccolo snares, specifically the standard Pearl one. That was my first snare "upgrade" back in high school and it made a huge difference over the stock snare that came with my set. You obviously won't get a lot of resonance or warmth, but it provides a great crack that cuts through anything.
One last thing I would suggest is the Musicians Friend platinum card. They've got ridiculously long zero-interest periods (as long as 48 months for some gear). That's how I upgraded my kit and I paid it off for $40 bucks a month over two years. I've made subsequent purchases of a new snare and recording equipment, too. I plan on buying a pair of Paiste 2002 hi-hats soon. I'll probably always be paying $40 a month on that credit card. But hey...no interest!
Also, check Craigslist for deals.