Regular oil and filter changes, won't do any harm to replace gearbox and Diff fluids, disregard BMW's fill for life mantra for these two items, they only advised that to cover the warranty period of the cars. Changing the gearbox fluid you will notice an improvement to gear changes.
Check what fluid your gearbox takes some use ATF. There would have been a label on the side of the gearbox detailing what fluid it takes but the label may well be long gone by now. Opie Oils is a good place to check what they recommend based on your model and ask for a forum discount if you buy from them.
The sills can rust at the front and rear but are cover sills and easy to unbolt if they need repair or replacement. Pays to take them off and inspect the inner sills for rust, treat any and apply Waxoyle or other rust protection before replacing the outer sills. Make sure you clean out the jacking points under the sills and apply Waxoyle behind the plastic jack insert.
Check out all the rubber suspension and anti roll bar bushes for wear. Usual checks for brake pads and discs, all very easy to change if needed.
Pays to check out parts suppliers like Carparts4less and Autodoc remembering to use their frequent discount codes. Carparts4less is the Web only site of Europarts and usually cheaper than Europarts, however you can order on line and collect from Europarts or have home delivery.
Check out the condition of the aerial grommet, if its damaged or gone very hard replace it but get it direct from BMW, eBay ones are expensive. High level brake light gasket can fail allowing water into the boot just like a failed aerial grommet. If these leak it will find its way to both sides of the boot well, battery side and on the passenger side drown the tilt alarm switch that lives at the bottom.
That's about it but bolster your toolbox with a good fault code scanner, I can recommend a Creator 310 or 410 for circa £50 eBay or Amazon.
For the Z3 you will need a 20pin to 16pin cable changer to plug the scanner into the round 20pin diagnostic socket in the engine bay to read all modules. If you also have a 16pin OBD2 socket inside the car under the steering wheel that will only read engine and transmission modules. The 20pin under bonnet socket will read all modules including of course the airbag modules.
to the forum from me too in Stafford.