I would say a free car should be a junkyard dog. I know drags aren't your thing, I but I have seen a ton of the Cutlass's on the 1/4.
They can also be done quite nice, unless you're married to the Mad Max look. That whole bit about the $50 roll on Krylon/Tremex paint job is a very Zen way to spend time with a car, but messy. I took this appraoch with my track bike, and was pretty happy with it.
Its the blue one. The green one has a very well done booth job over expensive race plastic.
The new cheap paint is the boat stuff, and I guess that can be found as well. Get a decent color, and then remove alll the trim bits. Spend some quality time with a can of black spray paint and you have a decent looking fun car.
You pull its are a great time kill as well. You can get the GM Rally wheels for the Olds, buckets seats were availible for those cars (if you can find them) but I think the Transmaro seats should fit as well, or even S-10 with some seat rail mods. If you can get a center console out of a simiiar Buick, Poncho or another Olds, you'll be on your way.
If the carpet is shot, the auto parts folks have cheap generic carpet availible in an y clor you need. I actually spent a weekend with this, and some interior paint on an old Chevy pickup I had and it really did do a nice job. Prep work is key. The outside was still crap, but the inside became a much nicer place to be.
The junkyard can also yeild all kinds of fun engine combos, not to mention the aformentioned trans as well as the rear end you are looking for. Of course a digital camera, tape meaure and a few good message board are you friend (case in piont). Even if you have no interest in making this inot a drag strip terror, those guys know all kindas of ways to make it quick, as well as the circle track folks.
Depending on your tow vehicle, get a set of decent rear tires and you can get a car dolly from U-Haul for less than $40. Pick the dolly up late the afternoon prior, zip out there and grab it and roll over to Bros house 1st thing in the AM, and have the dolly back at the U-haul before the 24 hours is up (depending on the distance).