If I had 10K to turn a stnadard car into a track car I would spend maybe 3K tops on the engine, and that would basically be to get it to a good stage 3 setup and a very good service (including things like head gasket), Id spend nothing at all on the gearbox if its working ok, get a paddle clutch.
Decent diff, decent rear beam, coilovers, and a really good set of brakes and a set of 888 tyres or similar