You can go to
www.discovernursing.com and click on Search for Programs to find out all the schools in your area that offer nursing degrees, and what type. If the school has a website, it will list that, too. Most school's websites are very detailed about what prerequisites you need for their program, and how to apply.
I would suggest poring over that for awhile. Map out what classes you need for which programs, tuition costs, length of program, etc. and narrow it down from there.
I know for me personally, there are 4 universities in my area that offer BSN programs. Three are private and one is public. They ALL have different prerequisite requirements! There is quite a bit of overlap, but not everything is exactly the same. I'm applying to 3 of those schools, so I am taking all the prereqs I need for all 3 of them.
GRE scores are just used for graduate school, so you're off the hook there, unless you want to try for a direct-entry masters program (where you enter with a bachelors degree in another field, and go thru their program to get licensed as an RN plus a MSN, without a BSN).
Good luck - it's exciting, isn't it?