Tire/Rims: My favorite resonably priced wheel is the ASA AR1. Inexpensive, well made and has that classic German mesh design. No need to go bigger than 17" with the 318ti.
www.tirerack.com is the place to search wheels.
Engine: Not much for these cars, except the Downing Atlanta Supercharger. There's always the classic intake and exhaust treatment, but the general consensus is that the supercharger is the only significant power boost for these engine.
Suspension: Being famed for their handling, thankfully there's plenty of suspension mods for BMWs. There's tons of info on springs and shock so I won't get into it. One cheap, effective mod is the BMW Motorsport "X-Brace". It's a factory part that will run you only about $100! It really tightens up the front end by tying the front subframe into the chassis better. It's quite noticeable when driving agressively. My other favorite cheap, factory modification is the ≥1996 M3 front control arm bushings. (the 1995 ones can be used, but the geometry will change up front, so you'll need to keep that in mind.) It was day/night difference compared to my old factory 318ti bushings. The M3 bushings are much beefier than the 318ti bushing so the steering feel got stiffer, but much more precise. Only about $45 for a pair.
Interior: The sport package (1996+) and club sport (1995) interiors are desireable. They have the cloth/leather sport seats and matching door panels.
Exterior is the same thing. The most desirable parts are the factory "M-Technik" parts that came on the Club Sport (1995) and Sport (1996) models. It includes the M3 front and rear bumpers, M3 side skirts and M3 body side moldings. There are aftermarket options too.
Welcome to the club!
Best modifications for the money? 
Linear Mode
