In particular, I found a 525i, but the ad mentions "brand new heads & radiator". Sounds like it had an overheating problem. Should I stay away from something like this?
You're asking good questions. Sounds like you'll make a good owner. BMW is a solid, strong car. The weak point is the cooling system. I doubt the engine was ruined and a new head/radiator was slapped in to sell. You never know though. Find out who did the work on any of the cars you're looking at. Ask for receipts. Read the invoices and note where the work was done.
I'd buy a car that was maintained by BMW in a heartbeat. There are some good indies out there as well.
The only reason I bought a 318i is because it's a manual trans and I paid a very nice price for it. It's a sedan, a family car. I do have some fun with it in 3rd gear on the freeway. The E36's aren't off the line cars. The freeway is where these cars excel. Mine just loves the open road. It eats hills. In town it's more of a dog. A very nice dog.
Gas mileage is much worse in town as well. So it kinda depends how you're going to use the car.
Much luck with your search.