I have an e36 318i. You can't get anymore basic than mine. I'm thinking about a few simple modifications to take it to the ring.
I'm not touching the engine, unless some simple parts need replacement, like filters or so. No big investments. A turbo could ruin the handling. And other improvements are just not worth it IMO.
First thing that will be done is a new (second hand) set of wheels. I'm taking those of my mom's car.

These are 205 in width. I'll let you know in a few weeks if it was worth it.
Second, when my suspension needs to be replaced, I'll go for the sportsuspension.
After that, well we'll see. Possibly a sportseat for the driver and a steering wheel which is a bit smaller and has better grip.
Oh yeah, and good tyres are indeed a good idea, especially for driving in the wet.