Wow..... That's a lofty goal!
Yes, you will need a lathe. In fact depending on what you make vs what you buy, you might want to get a lathe first.
If I were doing it (and I am not doing it), I'd make a component list and then decide what to source and what to make and maybe go from there.
Quite a few members on here make model engines and some are into R/C. Actually, I do R/C too (helicopters) but I buy my stuff already made. Anyway, my point is that some make engines and vehicle parts. You might do a search on radio or remote or model and see if you can find a few and then PM them. They could prolly give you better advice on priorities than I can.