I would say the most important thing when looking for an older BMW is to make sure that the car itself is rust free with good solid paint finish. Check the bottom of all door panels, wheel wells, rear trunk channels, all window seals, and especially the lower tail light areas where rust tends to start/accumulate.
Second, take a good look at the leather interiors. Comfort seats or sport seats, headrest, rear seats, leather panels, even the vinyl dash. Harder and harder to find a dash that is NOT cracked. I would say although there are parts still available for these E24s, it is the refurbishing of the interior leather, dash, seats and especially the rust (if any) and exterior paint that will set you back the most. The engines on these classics are near bullet proof and to get things repaired is marginal compared to the cosmetic issues that the older bimmers will have. I would have to agree that $5500 for a US 633 is on the high side (I got my Euros for less), but if the car is solid inside and out, near concours. It would be a fair price. Nice Euro models will go for $7500+ and M-Models will hoover in the $12K-$20K ranges, pending condition of course. Really nice, clean and low mileage M635csi models will go $20K++.
Make sure you take the car into your mechanic shop to check the usual things...brakes, exhaust, heads, suspension, fuel system, engine cooling system, bushings (if manual).
Good Luck on your pending purchase. AND welcome to the madness!