IMO wheels/tires would be the best way to start. Go for the factory sized 20" 275/40 and 315/35. Add spacers if necessary.

The smarter idea would be to put the money into some preventative maintenance. The cooling system is likely do for some work, suspension too.

Looking good as is, cheers.

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2002 X5 4.6is - Titanium Silver / Black Alcantara - Dinan Stage 2 - Bilstein/Eibach - Brembo BBK ----SOLD---
1993 318i - Brilliantrot / Tan - bone stock daily driver