Just got back from picking up a 1986 gsxr750 to rolling chassis. Not sure if I'm going to build a race bike out of it or street bike. But sure will be picking y'alls brains for ideas and sourcing parts. Build date on it is 12/85.
I would look at picking up a Katana 1100 and transfering the engine, forks and wheels to the GSXR. I think it would all be pretty close to bolt up. Old Katanas, 1100 or 750, are pretty dirt cheap on craigslist.
Whatever direction you decide to go, I can answer most of your questions. As for the front forks they will be fine if you street it but if you decide to track it then find 88 or newer forks. You'll need triple clamps from whatever year forks you'll buy but it's no worries as they all bolt up. Newer forks allow you to go to a 17 inch front wheel without having to change bearings and build spacers. As for the rear, any 88-95 will work but you will need to get the cush drive and sprocket carrier as 86-87 are different bolt pattern. Keep your spacers, you'll need those as well. Let me know what you need as I've got some spares I can make you a good deal on. Eric Bozell Eboz