w/o knowing the year, mileage & service history it would be difficult to say. looking at the pictures, the car looks like an older e39 sport w/o vanos. general issues to start would be the complete cooling system replacement, if you are already planning on replacing the waterpump, replacing both valve cover gaskets, replacing coil boots & plugs, o2 sensors if old, fluid change. good luck.
'00 TiAg 540iA Sport, '90 325i, '01 325ci