Buying a house AND car is a big expense why not just buy a car and learn to drive it if you actually have somewhere to park it. Theres also mobile homes and RVs.
if its an aprtment in the city you wont really need a car.
The other thing is you could bike if you dont have a bike already. in terms of independence if you dont want to use public transport, though you do need to be road savvy using
it.
homelessness is a big problem theses days. Be thankful you can stay at home and your parents love you and want you around. If they not treating you badly then why not stay?