Here's a little bit on wheels:
E24 6 series come with metric wheels. They're 390mm (15.3 inches) in diameter and require a specific metric 'TRX' type tyre. They are expensive at around £200 each so lots of people (including me) swap the wheels out for imperials since a second hand set can be bought with tyres for less than the cost of four new metric tyres alone.
Just to state the obvious, you can't force fit a 15" or somehow pad-out a 16" tyre and make it fit a metric wheel.
If you want to replace them look for some off an E34 5-Series and go for 16 inchers. They fill the arches a bit better without putting undue stress on the suspension and various other bushings.
No E36 3-Series wheels will fit - they have a different stud pattern
If you just want some that go straight on then you need to look for wheels that are 16x7J ET20. This means 16inch diameter, 7 inches wide with an offset of 20mm. The offset determines how far off the dead centre of the wheel the cars hub will meet it and is very important. Even wheels that are the correct width could end up too close to the suspension cup or the wheel arch if they have an extreme offset.
I picked up a set of "turbine" BMW wheels with usable michelin tyres off ebay for £150. It turned out that this was only a partial success because the E39 has a larger hub diameter than most other BMWs so I could never get them centered and my steering used to wobble like crazy above 50MPH.
This was easily resolved by fitting hub-centric rings or "spigots". If you're going this route then you'll need to get hold of some 74.1mm to 72.6mm rings. A pack of four should cost around £20.
