I would recommend first to fix anything that is wrong with the car mechanically first. Assuming that has happened...
Get a new set of shocks and springs. I got H/R and Bilstein for my e30 318. you might need to read more about what would be the best bang for your buck on an E36. Will make the car handle much better, and although it wont go faster in a straight line..it will turn a lot better.
if that is not what your looking for I would look into engine software upgrades. Dinan is good.
Exhaust/Intake. (im sure someone on here can give you good name brands)
Overdrive pullies. I had UUC on my 330. They were a good upgrade for the money.
anyone else? You could start doing internal engine mods...but that might end up being more then $2000.
Suspension mods should be 1st, I would start with shocks and Springs, Bilstien sport shocks/struts are nice and H&R Sport springs would probably be a nice upgrade.
Someone else suggested maintenance I think that's a really good call, especially if you don't have records for the car or know when routine maintenance was done. This way you have a good base for the car and you will hopefully save you some cash in the long run.