You can use whatever place you want as a place of business as long as you are legally allowed to do business from that location and you have some sort of agreement with the owners to actually do so (a lease for example).
The ATF couldn't care less where you do business as long as it's legal.
You will have to keep in mind that part of the application specifies hours which you intend to dedicate to your business. These are the hours that the ATF can (and will) show up unannounced at your place of business to do inspections.
Do your parents want the ATF showing up unannounced at their house, looking for you, your guns and your bound-book?
It's obvious that you are early in this process but just take care to learn everything you need to know before you get started. It's not that complicated but there certainly are things that you need to know and you need to do right.
Still happily answering to the call-sign Peetza.
The problem, as you so eloquently put it, is choice.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.