501(c)X is a Federal determination, not state.
Correct. But you also typically have to be a non-profit under the State's rules also for State taxes (if any), etc.
The advice to find an Attorney and pay them to get it right, for your State, can't be stressed enough. Especially considering that the laws surrounding the "corporate veil" have been so weakened that it's almost not worth being involved in Non-Profits in a leadership role, since your personal assets are at tremendous risk if another Board member does something stupid.
Speaking of that. Carry liability insurance for the Board. Don't make them go out and buy a rider policy to their Homeowners or similar for their personal liability as a volunteer willing to run your club.
Many people with significant personal assets (and thus, great management experience and advice), are avoiding working on Boards of Directors for Homeowner's Associations, Civic Clubs and Organizations, and other Non-Profits because they don't want one yahoo on the board getting them sued and having to spend significant money defending their personal assets from a negligence suit.
Often-times these liability policies are very inexpensive and also cover liability for things like meetings, in case some club officer or BoD member did something silly like string a power cord for the night's presentation to the projector, and a member trips over the thing and injures themselves... just paying to defend against that suit could bankrupt many small clubs.
Look into having one. Marsh is one provider I've seen used successfully for such things.