Welcome Christian and congratulations on your 944. It sounds like you got a pretty good deal.

Can we assume your looking for street wheels? Something that looks nice and fits? Or are you looking for a set for the track? What kind of wheels did it come with - Phone dials? The 15” and 16” phone dials make for pretty good track wheels. They’re lightweight and pretty cheap to replace. Lots of tire options in 15” too.

Any of the late-offset 944 and 951 wheels will fit your car. Also, 968 and some 993/996 wheels will fit. The offset your looking for is 52mm front and rear. You can have a little more offset and/or install some spacers if needed. Without any modifications you can fit up to 18x8” in the front and 18x10” in the rear, but I’d recommend 17” max if you can find them. Also, you don’t really need more than 8” wide (7” are fine) front and rear unless your using them of the track. There are lots of 18” options for sale on CL and here on the forums. The 17” wheels are harder to find in the correct offset. Look in the Parts Market.

I agree the 16s are probably the best stock size for the 944 - street or track. I have a set of the five spoke 968 wheels on mine. Unfortunately, tire sizes are very limited for 16” compared to 15”, 17”, and 18”. IMO the 17s look nicer and the 18s look awesome, but they’re often too heavy and too wide for this car.

There are a lot of Cayman wheels available used on CL. You should be able to find a set of 4 for about $500 in good condition. Maybe you’ll get lucky and the tires will have some tread on them.