You may not work in the US without a proper guest worker visa. A B2 visa is for visiting. Working while in the US on the B2 visa is illegal and can have long term consequences for you. Illegal work is viewed to be a serious violation of your B2 status.
Continue with your original plan of applying for an F1 visa and enter only to begin your classes. Note that only limited work on campus is permitted on the F1 visa but it must be authorized by the university. You may not babysit for your friends while on this status.

