I have a 91 (E30) 318i... It has the M42 engine, which was the original, 1.8L version of that engine... Its a good engine, and the e36 model is a nice car... definitely worth taking good care of.
For motor oil, Id use Shell Rotella synthetic 5w40. Im using it in my 318i, and the results have been excellent, Ive been very happy. Protects well for our climate, and is good as a year-round oil, as it flows better in the cold and hot at startup. Oil analysis results have been great, and the oil is a great deal at walmart. Be sure to use Mahle filters, by the way.
I assume that it is manual transmission, and that the trans takes ATF. id suggest that you replace the fluid in the transmission and especially the differential. I currently have redline MTL in my transmission, and redline 80w-140 in my diff. Id suggest using Redline MTL in the trans and a 75w-90 or 140 diff oil, either redline or mobil 1. If the car is an auto trans, replace the fluid... Id suggest you go to BMW and buy the correct fluid as auto transmissions can be picky.
Flush the brake fluid. BMW suggests ONCE A YEAR! Try andget some ATE SL DOT 4 fluid, but if you cant source it conveniently, either buy from BMW, or get valvoline synpower.
Flush your coolant. Be sure to use the G-48 formulation, which is BMW BLUE. There is no cheapo substitute, so go to the dealer and buy two gallons... Flush it well, maybe twice, as mixing antifreeze chemistries isnt a good thing.
Check the tire tread depth since winter is coming and BMWs arent really good in the snow... and make sure theyre inflated properly for optimal MPG. Of course, also check brake pads...
Other than that... maybe an air and fuel filter, and youre good!
I wouldnt use a lot of cleaners... If anything, Id put a dose of techron in it as soon as you get it (maybe try and add it to a tank thats not full so its more concentrated), and then drive a while... Change oil as the last thing you do. LC and FP are smart in any car!
Good luck!
JMH