Congratulations on the ride. I've owned the same car for 3 years, 'cept mine's black. I got it shipped from AZ to Cali. It's my first and only car I've ever owned. I've done PLENTY of work on it (I bought it off ebay) and now I finally have it in decent running condition. You're fortunate that car had a good owner, let me tell ya! As an aspiring BMW technician at Wyotech, I've learned a lot from working on my car. It means a lot to me, so don't hesitate to ask if you got more questions.
The profile gasket on that car would have failed long ago if it was bad. They were known to go out after 75,000 miles, so you should be fine. The reason the car takes premium is because of it's 10.5:1 compression ratio. It has no knock sensors either.
If you're having a stumbling idle, check for vacuum leaks. Look for cracks in the intake boot, the ICV (the small metal cylinder closest to the firewall, right behind the cylinder head) vacuum hoses, the vacuum hose underneath the intake boot, PCV hose, hose couplings underneath the intake manifold (if cracked, can leak oil/coolant onto the engine's wiring harness).
Replace the timing chain tensioner (hydraulic, costs less than 50$, is a 10 minute swap) if it hasn't been done so yet. The stock ones were not a good design, and you can no longer buy them. BMW has updated the part. If you hear a high whirring sound from 1500-3500RPMs, it means the timing chain components are worn, which is another issue with these cars. The engine is of the interference type, but the chain is not likely to snap. However, timing could be affected, and that noise is very annoying (still have to do mine =(). It's a huge job, but can be done in one's garage with the right tools. However, if your sprockets/rails/chain are all worn, it could cost upwards of 800$ for just parts.
Try a good top engine clean, that did wonders for mine (if you don't mind lots of smoke for about 20 minutes =)).
Spend about 20 bucks at Autozone or equivalent on a 16oz can of SeaFoam, and some fuel injector cleaner like Techron concentrate, Redline R1 or what have you. Drive the car until the engine is plenty hot. Park the car and have someone hold the RPMs up to about 1500. Remove the vacuum line that leads from the purge valve on top of the charcoal canister and leave it plugged into the intake manifold. With the engine still at 1500 RPMs, start to let the manifold vacuum from the hose suck up the SeaFoam. The engine will start to stutter a bit and want to die. This is normal, but don't let the engine die on you. The idea is to suck up about 3/4 of the Sea Foam so that it sits inside the combustion chamber and soaks into the carbon deposits in your engine. Once there's 1/4 of the can left, let off the gas and completely submerge the hose in the container of Sea Foam. This will make the engine shut itself off while sucking in the rest of the Sea Foam. Let the car sit for about 30-45 minutes and start it up. White smoke will start dumping out of the tailpipe. Drive the car through the entire RPM band until the smoke is gone. Then dump the fuel injector cleaners in your tank. All of this will increase performance and gas milage while decreasing emissions. http://www.esatclear.ie/~bpurcell/index.html
<--- Plenty of good info on e30 318is.