I have an early '70's SAAB 96 works car and you can pick up almost any 'normal' 1960's -1970's rally cars for under £10K. I'm not talking about a Stratos here

But Mini's, Escorts, Cortinas, Chevettes and Mantas are pretty affordable. But they are road-legal racing cars, not runabouts - that's why the car was detuned for your Nan to run it.
Personally, I would not attempt to rebuild that bodyshell, but I would find out EVERYTHING about the car. If nothing else, it'll be a fabulous bonding session between you, your dad and your grandad.
If it does have genuine race-level tuned parts (engine, gearbox) then those parts may well be worth salvaging, either to sell and fund another vehicle or to transfer into a new donor shell.
As a first car, any 1960-1980's race-level tuned vehicle is going to be very difficult to drive on the road. Typically they have extreme camshaft profiles and they don't tend to come 'on cam' until late in the rev range. They also tend to have special gearboxes that will survive massive abuse, but won't do anything for your reputation as a smooth driver.
I can remember this phase in my own driving history - my dad had had tuned cars, so I wanted tuned cars. I pumped everything I had into polishing a turd. It was still a turd and it expired in a huge puddle of oil and smoke on the M8 one Saturday night. My girlfriend heaved a huge sigh of relief
When I could afford it, I bought a proper one
Do yourself a favour - get something modern. But standard! A small hatchback with a big diesel engine in it will generally get you where you want to go with a smile on your face without costing a fortune to run.