What model replacement radio does this car need?

That depends on what features you want. Do you want it exactly stoc, or an aftermarket model?

My favorite source for aftermarket car audio is Crutchfield. You get a complete installation guide with every head unit you buy. Some even come with a complete install kit, if one is needed, plus the wiring harness adapters.
http://www.crutchfield.com/App/Car/outfitmycar/MyCar.aspx

Hopefully, it saves the vehicle lookup information and takes you to the landing page that gives you the options that give an exact fit for your application.

I just want a replacement like the original model. They seem to be readily available but I don't know which model to search for.

If you want the exact model it has now, you need to pull the old one out and check the manufacturer's tag. If you just want one with similar features, then you need to search by those features. We have no way of knowing if the original owner specified certain features or just chose the base model. We have no way of knowing whether it's a Blaupunkpt or an Alpine. Take a look at the link below. It shows how many different model #'s were available on that year and model.
http://data.bmrparts.com/bmwparts/1319.html