Check for cracks near the bolts holding the engine mounts to the front subframe. Some of the heavily tracked M3's are showing cracks there. You can see the cracks from the underside of the subframe at the bolt locations. The cracks are in the subframe metal. Shake the engine vigorously and if you hear a squeaking sound, the front subframe is probably cracked.
Check for dimples in the roof between the windshield and the front edges of the sunroof. This is another sign of a heavily tracked car. The dimples are caused by torsional stresses on the body.
Common modifications are a performance chip and modified exhaust cam gear. I have some personal opinions on the various chips for this car. E-mail me if you're interested.
If you are going to drive the car on the street, stick with the stock suspension. The aftermarket performance suspensions are too stiff for the street. The OEM suspension is fine for both street and driver schools (but adding Bilstein Sport shocks really improves track performance). There are BMW factory "camber correcting upper strut bearings" that will add .5 degree of negative camber to the front suspension. They make a tremendous improvement in the way the car corners on the track.
If you take the car to driver schools frequently, you should consider ducting the front brakes by replacing the foglights with brake ducts. Without brake ducts, the rotors tend to warp on the track.
Plan to buy a new water pump every few years. For some reason, the E30 M3 engine wears them out quickly. The M3 does not have the coolant leak problems of the other E30 models, but some of the M3's experience coolant loss from a worn coolant recovery tank cap. Buy a new cap from the dealer. The new ones have been "updated." There was also a recall for a cooling system update which consists of a special valve that was installed in one the of the heater hoses that runs from the cylinder head into the firewall.
The lower control arms tend to crack on heavily tracked cars. The aluminum alloy control arms can be purchased mail-order from Eurasian for about $159 each. They also sell the offset control arm bushings for about $89 a pair.
There is a lot of disagreement on the best brake pads to use. The OEM BMW pads (Energit, not Jurid) seem to work fine for street and driver schools. I would recommend using the Energit OEM pads unless you are racing.
The Bentley manual for the E30 BMW covers most of the same body and electrical as is on the M3, but the engine and Motronics on the M3 are different. The factory service manual (on microfiche only) is the only thing available on the engine.
Are the swaybars still stock? If there are stiffer aftermarket swaybars on the car, you should take a close look at the mounting locations. The mounting tabs on the front and rear tend to crack with stiffer bars. The tabs need to be reinforced with extra welded metal if stiffer bars are installed.
When you have the engine inspected by a mechanic, have him/her remove the valve cover and look carefully for wear in the chain, cam sprockets, and chain tensioner parts. These parts are wearing out on the higher mileage cars.