Nice lookin Z3! E36/7 chassis. What year, 99-00? The 2.3 manual tranny cars are fun! They scoot pretty good too. I originaly didnt like the Z4 but i like them now. Yours has some decent factory wheels too.
We have a customer that had a 2.3L Z3 that had some aftermarket road race parts and he roasted his motor. Instead of another 2.3, we found him a 3.2L S52 motor from an M3 and i did the install/conversion along with more upgrades, its one nasty machine now!
Just some recomendations (fac cert. BMW tech

)
BMW synthetic 5w40, change every 6K or 6mo, factory drain is too long, IMO
(and to save a buck, BMW factory oil is Castrol Syntec)
Check condition of the belt idler pulleys, tensioners, water pump.
We have seen alot of these motors cooked to death when a pulley comes apart and the belt falls off. There always noisy and loose if there bad.
These cars run the best with the factory NGK BKR6EQUP spark plugs, there not cheap but last along time. There a 4 electrode plug but they are far superior to the crappy Bosch platinum-4 that alot of people install.
Common for the lower intake boot to develop cracks/holes in the little elbow for the IAC inlet, makes a sqweak at part throttle if bad. M52TU-M54 engines only
Not tryin to scare ya, just helpin, feel free to ask for more if ya need!