To make this a "realistic" budget build, include the market-value of whatever parts you use, whether you got it for a steal, or it's been in your way in the garage for the last 15 years, go by what the parts are worth. The only parts you don't add to the cost are the ones that came attached to the car when you got it.
A $10,000 budget is pretty tight, but completely feasible if you don't get too crazy with anything, and are OK with buying or re-using some existing used parts. Brakes, for example don't need to cost a fortune.
4-wheel discs for well under $1000. Sure they're no 13" C5s, but the budget probably can't support those.
Other ideas to help give the project some direction:
For wheels, something like a 17x8 AR "Hopster" would look good without breaking the bank, give it a Pro-Touring flavor, and they're not TTIIs.
Engine/Trans-wise, I'd stick with an Olds 350/TH350 for a cheap combo, but if it's in the budget, an LT1/4L60e is hard to beat if you want injection and O/D, gas mileage, and reliable power. It's not an olds motor, but it will bolt right in.