Hi,
Depends on how serious you want to get but the basics you will need are:
Uprated brake pads, I import and sell the Porterfield pads which we use on our race cars http://garagewhifbitz.co.uk/category/whifbitz-cars/
You can see the prices for the the pads here http://whifbitzperformancetuning.co.uk/toyota-supra-supra-brake-parts-brake-pads-c-42_47_76_877.html
Motul RBF660 brake fluid and braided brake lines http://whifbitzperformancetuning.co.uk/toyota-supra-supra-brake-parts-hosesfluid-accessories-c-42_47_76_77.html
Suspension wise, it really does depend on your budget and again how serious you are going to get. I've sold and fitted LOADS of BC Racing coil overs and never had a bad thing said about them, only positive, they offer amazing value for money. At the other end of the scale you have Nitron which we developed with them for the Supra, all can be seen here http://whifbitzperformancetuning.co.uk/toyota-supra-supra-suspension-parts-coil-overs-springs-c-42_47_838_840.html
Titan anti roll bars are highly recommended to, http://whifbitzperformancetuning.co.uk/toyota-supra-supra-suspension-parts-anti-roll-bars-strut-braces-c-42_47_838_839.html
You should also have your suspension arms checked for any play, especially the rear upper arm bushes, these are a common fault now, as the cars are getting older.
Cooling wise, you should definately fit an oil cooler, http://whifbitzperformancetuning.co.uk/toyota-supra-supra-cooling-parts-coolers-power-steering-tanks-c-42_47_473_475.html Something like the 25 row cooler would be a good idea on a BPU car. Stock radiator should be fine as long as its in good condition and not blocked.
Other than that, wheels/tyres, bigger brakes, more power, making the car lighter, decent seats with harnesses, a decent diff unit, aero kit, etc etc.
We can supply and fit all of these parts of course.
Any questions just give me a shout.