I lived in NY for most of my life. Moved to PA a few years ago, but i still work in NY (Orange County). If you are 21 and you are not legally barred from owning a gun, you WILL get a pistol permit. Some counties are "May Issue", and some are "Must Issue" regarding concealed permits, but you will get a pistol permit when you are 21. While some idiot jude MAY tell you you don't need to carry for protection, NOBODY is going to say you can't shoot at the range. And using a range gun for home protection is fine as long as you tell the cops that you heard the noise and then loaded your gun. Bad guy is either gonna be dead or not believed anyway.
As for gun choice, if i still lived in NY, as far as semi autos, I'd go for a 1911 first. Classic gun that belongs in every collection and it complies with the law. After that, a new semi auto that is standard 7 rounds like the M&P Shield. But a revolver is a GREAT first gun to buy, and as others have said, do NOT overlook the Ruger GP100. For a NEW revolver, there is no better. New S&W revolvers have the lock, the frame mounted firing pin, and the MIM parts. Sure, they work, but they're not up to par with the older ones. You can get a PRISTINE used 686 for about $650 if you must have a S&W.
And i agree the fees can be steep, but put it into perspective. How much you spend on your cell phone every month? bet you have a game system and several games, too. Spend the cash if you need to.