Hi and welcome to the forum Frustrated!
You didn't specify but I'm guessing you are looking at the 3.0Si Coupe rather than the M!
I had two 3 litre ones for 5+ years and loved them both, but there are a few things worth looking out for. Some owners suffered from rusty tailgates and a few were replaced by BMW under warranty, but as that lasted 12 years from registration most will have expired by now! When it is open look all round the edges for any signs of corrosion. Rear brake pipes can corrode (don't ask how I know) just in front of the passenger side rear wheel. There is a plastic cover under the passenger seat area and road debris builds up in the end of the cover and holds moisture with the inevitable result!
They use the N52 engine which has an electric water pump. The issue with that is it doesn't leak or screech like a mechanical one, it just stops working and the temperature goes from normal to the red in about a mile and you don't want to drive it like that although it will go into "limp" mode if you do. The downside is new OE Pierburg pumps cost around £300 (or £500+ if you buy from BMW). How long it takes is like a bit of string! My 1st Coupe needed a new one after 10 years and 60K miles but my 2nd seemed to be on the original after 90K and 13 years. Whether you do it as a preventative measure is up to you, but might be a good idea if you are planning a European trip. The N52 also has no dipstick, you check the oil level using a button on the dash which isn't really a problem but you need to get used to it.
BMW claim the transmissions are sealed for life, but I had fresh fluid in my 2nd one at around 80K and I think it felt a bit better afterwards. But at the same time I fitted a ZHP gear-knob which is a bit shorter and heavier than the standard one so that would also have helped. Getting the Clutch Delay Valve removed is also well worth doing as the clutch take-up feels much better, but both the latter 2 items only relate to manual ones.
The Diff is also sealed for life, and as I was told it doesn't have a drain plug getting the old oil out would be quite a challenge so I left that.
They can suffer VANOS and CCV problems but I wouldn't start swapping any of that unless there was an issue, and coil-packs will fail from time to time like most cars. The engines are also prone to leaks from the cam-cover gasket and the oil filter housing, but it's pretty obvious if it is leaking - neither of mine did!
Lastly you need to bear in mind that only just over 3,000 3.0Si Coupes were registered in the UK so you might need to travel to find the right one. There was an SE model, but most people want the Sport because it came with the sought after M-Sport seats as standard - as well as M-Sport suspension (15mm lower and stiffer) and M-Sport steering wheel. Factor in things like colour choice and options and the numbers diminish quite quickly. Especially as things like Cruise Control, Bi-Xenons, heated seats, rear parking sensors, cup-holders, Multi-Function Steering Wheel were all options although Cruise and cup-holders are easy retro-fits. All Coupes had electric seats with driver's memory though.
Hopefully I haven't forgotten anything, and good luck with your search.
