I would check all the things you mentioned including the battery. Have the plugs been changed? Check all the fluid levels I.E. oil, PS, brake fluid, etc. If you are doing the work yourself get a Bentley service manual. Things to watch out for are worn rear suspension parts. I own a 2000 323i and have replaced cracked rear coil springs, rear sway bar links and rear shocks. My car has approx. same mileage, too. Good luck and have fun with your car they are great cars!