PhD programs are often fully funded through: outside fellowship (NSF etc), university fellowship, or getting a tuition waiver and a RA/TA job offer to pay a stipend you use for housing etc. MS are often self pay although some schools may offer scholarship full or partial and some schools may have a work for you.
you want the strongest gpa and gre you are capable of. Tis and research is what grad schools want to see, why you are interested in research what you have done and letters from professors who worked with you on research and can attest to your capabilities for that as opposed to getting good grades in class.
Out of state isn’t much different than in state. Grad students can live in grad housing if available, but just as often share houses and apartments and you find it through school listserves or BB boards or craigslist like anyone else.
The best grad programs is something you can google, but usually there is a best ‘fit’ for you in terms of the type of research interests you have and how that fits with profs at various unis and research groups there. Often there just isn’t an ultimate best but a group of them.