When I moved out of my parent's home for the first time I was 19 years old and I moved from Hollywood, FL to Hollywood, CA (with my cousins)! Being an easy bike ride will be a plus for those times you feel like getting away from being away. Trust me, you'll understand.
Sounds like you'll be close enough that the bouts of home-sickness will be easy to deal with.
And yes, learning to work within the parameters of a budget when you are young is the best way to make it a life long habit!