If your just buying the supra now.. I would read a lot..
Check the wheel wells very closely (you are in Florida, so rust isnt going to be as bad of an issue as up North.. depending where the car came from). Also, put your hands in the rear quarter panels (you can access from inside the hatch) and feel the bottoms.. if full of dust/moisture.. your going to have to look at everything for rust. Dont forget to pull the spare tire out and see the condition of its holding area as well. Water will pool there if your brake light seals/hatch seals arent working perfectly.
As for the rad support, I have never personally seen rust there except when the metal is kinked. I will have to let someone else answer that part.
Just as a further note.. I went to buy a 90 Supra for 2500, and ended up buying it for 800 after I did a full inspection (for body filler etc..) as these vehicles have very well known areas where they age faster.. Doors, Quarter Panels (above the wheel well), mud flaps and trim, body trim, brackets that hold the bumpers on, etc...
Do as much reading as you can prior because it will save you a lot of time after.