For schools that use FAFSA only, or explicitly state that they do not use non-custodial parent information, your financial aid would be based on the parent you live with. For other schools (i.e. that use CSS Profile including non-custodial parent information), your financial aid would be based on both parents. Note that income and wealth of current spouses (if any) of your parents are also included.
Note that many of the “meet full need” schools do require CSS Profile with non-custodial parent information. Also note that “meet full need” schools vary greatly in terms of how much financial aid they may give, since each can define “need” any way it wants, and each may have a different student contribution (student loan + student work). Run the net price calculator on each school’s web site to get an idea of what it is likely to offer (and pay attention as to whether to use one parent or both parents for the net price calculator each school). If the net price calculator indicates an unaffordable amount, then you need to check whether you can get a large-enough merit scholarship at the school.