PS- This will not be a carry gun, simply a range/hobby firearm so stopping power is not a concern for me.
This comment pretty much says it all. A 22 Rimfire would be a perfect choice. Especially with you being a brand new, inexperienced shooter. Easy shooting, much lower cost of ammo (it will be available again). Lots of learnin', shootin', and fun for the money.There will be time to move up to a centerfire some day, even in NY.