Gen 1 CTSV’s came with either the LS6 or LS2 depending on model year. It’s an obnoxiously fun car but it’s a Cadillac with a Vette engine slammed in there. Bushings are all soft and the rear ends were prone to bad wheel hop as a result. I sold mine while it was still clean and relatively unmolested and actually made money on it. Good examples are still going for 12-17k as the early V2’s prices are hanging in the high 20’s and low 30’s.
Honestly for 10k it’s going to take a search for a good example these days, but it can be found, is hands down the most enjoyable car to drive I’ve owned is an E36 M3. Cold air intake, OBD1 intake manifold, headerback exhaust, chip and then just about every urethane bushing known for those cars paired with a set of Bilstein Sport struts and H&R race springs made for an incredibly fun car. Do the cooling upgrades that they need, which at this age now is possible it’s already done. Service the Vanos and get a Turner diagnostic tool and it’s just as easy to work on these pre digital everything BMW’s on your own.