If a PO used high phosphate coolant it will chemicaly damage an alloy radiator byond repair - new core. Does it have a fan clutch? If so change it. +1 on the other suggestions.
Good - Fast - Cheap: Pick any two.
E23 735i; E30 318i; E32 735iL (X 2 - 1 White and 1 Light Blue); E34 535i; E38 735iL; R50 Cooper; R55 Cooper Clubman.
E21 318i; E32 735iL; E34 535i; E38 730iL; E53 4.4i