It's been over 10 years since I lived and worked in NYC but I remember it being a PITA to own a handgun there and so I never did, but I defer to anyone who knows current requirements. There are definitely gun shops in Mount Vernon, New Rochelle, White Plains, Stamford, Norwalk area and I'd recommend checking those out as well as local ranges where you can rent various guns and try them out.
You are correct that NY state limits mags to 10 rounds and yeah that kinda makes double stacks pointless for you. Single stack 1911 in 9mm uses a standard 10 round mag and even in .45 ACP, my Wilson 10-round extended mags (compatible with any make .45 ACP 1911) work great and I've never had a jam. But you need to put some rounds downrange in various calibers and see what works for you. 9mm is cheapest and most popular by far and is around 25 cents/round, about half the price of .45 ACP.
You'll also want to budget and plan for regular range time. Rifles are like riding a bicycle but you're not hitting jack with a pistol if you don't train with it regularly.
Depending on your preferences, you might also want to consider a revolver. Simpler and more idiot proof, it's an elegant weapon for a more civilized time. If so, I recommend the Colt Python, which like all .357 mag revolvers, also fires .38 special. And while not QUITE as fast as mag reloads, speed loaders or moon clips are still pretty damn fast. MSRP $1.5K. Or if you really want to ball out, Korth revolvers (available in the U.S. through Nighthawk) start around $3K. But like
@Protectandserve said, I'd recommend spending a lot of time training and trying stuff out before even thinking about spending that much on a handgun.