THe cheap cars will be Autos with over 150k miles. Because the transmission will be having issues. That is why 5 series are so cheap, due to the $3k repair bill for a Auto trans rebuild.
the cheapest 3 series will be a 4 cyl E36. The 318ti are not bad cars as long as they are manuals. They are not fast but they have a 50 50 weight distribution and handle great. They are pretty much the same under pinnings as a Z3.

The M3 E36 are great bang for the buck. But a cheap one is going to be ragged out and M parts cost more. Is in Suspension bushings etc. IMHO your better off spending more and getting a low mile cared for M3.

I have a few E34 5 series. My wagon has a S52 M swap with the manual. It a fun car to drive but only gets 14 to 17 MPG around town. The 5 series will have electrical issues, like power locks, headlights, etc. But all of this is documented on the internet and not hard to fix.

With gas going up you may want to really look at the 4 cyl cars if you are on a budget.
You can also find the old 320s from the early 80s cheap, but they will need work. THey are very basic and easy to work on, but they are SLOWWWW.