New to Us Supra Sport (454 V8) What Should I Know

Ian,
Congrats on this purchase, however, this could be a blessing or a curse depending on how your attitude is. You have one of the first production model Supras built in October of 1982 so when you say the hull in great shape, does that include the stringers? Because that is the only thing that matters to start with on a 38 year old Supra boat. Supra stands for Something Underneath Probably Rotten Already.

They were made of wood and poorly done to begin with and add in foam that absorbed water, if they haven't been done, there is no way they are still solid at this point.
If you know for a fact they have been done, then you're ahead of the game and that is the major blessing. If not, you will feel cursed when you realize the boat needs to be torn apart to re-do them completely.
Start with trying to tighten the engine bolts and see if they are tight or just spin. If you have soft floors, sure indication that they are rotten. Can poke around with an ice pick also.
You may / will have leaks around the exhaust ports on transom, shaft packing nut and/ or rudder. They will all need to be looked at thoroughly before launching.

I'm coming from experience so I would start here and then worry about motor because if you have rotten stringers, you will have to decide if it's worth your time or money to restore. You can spend easily $3-5 grand on doing the stringers. The motor will need to come out to restore and that's the best time to work on it.
If you search this forum, there are lots and lots of threads on stringer repair.

Good luck!