To get started, can I just run normal "speed rated" street tires as long as the speed rating is higher than my maximum observed speed, and weight rating is not exceeded? Y-rated would get me into "parachute territory"?
The simple answer is no.
The questions that need answered is what class are you planning to run, with what organization. 130 club for USFRA, sure, no problem, Bonneville, you must run tires rated for the record in your class. Get a rule book, read it 10 times, read the definitions and class rules, read, read and then read it again. Have you looked at a lot of cars, looked at cars in your class, give us a bit more information and we can help you. Don't remember your introduction, but help us help you.