I have a 1982 camaro berlinetta v6. My uncle owned the car since it was brand new. It is looking a bit rough and worn out, the paint is peeling and is faded, and the interior is falling apart. Being that it is looking the way it is I was planning to turn it into a sleeper. What I want to know is what engine, trans, and rear end should I put into the car. I would like to keep this to a budget less than 10k.

Engine - Any SBC is the easiest and cheapest swap and a 350+ is better than a 305 since you're going from a V6.
Trans - For street driving a 700R4 is the best choice.
Diff - There is no budget swap. The stock 7.5" 10 bolt was never made for performance. The cheapest swap would be an aftermarket direct bolt in 9" and that will start at around $1000 but expect to may much more before the swap is finished.