One thing to consider: A .223 round actually penetrates fewer walls than a 9mm. evaluate your surroundings and see what will be around you if you need to deploy your system in the house.
Here's a decent 9mm AR-15 style carbine.
If you want a cheaper alternative but still a 9mm carbine you could get a Kel-tec SUB-2000 or a Hi-point carbine. The Kel-tec comes in different models that can utilize the magazines for other pistols: Glock, Beretta 92, or S&W 59. (off the top of my head, I heard a rumor they were doing SIG mags too).
If you want to go for an AR in a pistol caliber the Lone Wolf Glock lower receiver simplifies things (See
here). It uses Glock mags so you don't have to get Uzi or grease gun mags (Not sure how available 10 rounders are in those models). Two things here can happen.
- You buy a complete lower, nothing else has to be done. Get it shipped to anyone with an FFL and fill out the proper paperwork and any other NY stuff that you need to do
- You buy a stripped lower and then get a lower parts kit and put it together yourself. There are videos out there and I have done this myself. If I can do it without making metal spontaneously combust with my mad Murphy's Law skills any one can. (I was chasing a little spring detent all over the place for almost an hour )
Then search for a 16" barreled complete upper. This is the modular and more affordable way to go if you can't shell out the cash for one in your state or online and have it shipped.
Keep in mind if you use a standard AR-15 you can get conversion kits to use .22 LR ammo as there are .22LR magazines that fit the AR mag well. Not sure if there's a conversion kit for the Lone Wolf lower.
Hope that starts this in the right direction. Remember to check about NY law before buying anything.
Edit to add: For a starter AR-15 check out
Del-ton. Pick your style and make mods if you want. They use quality parts and are about on par with Bushmaster quality if you ask me. I've got two, one runs like a top, the other is new so I have about 500-700 more rounds to go through that before I can say anything. Note: that link is for the uppers only, you would need to acquire a lower (stripped or complete) to put those on. Great thing about the AR is you can buy different uppers and they are not considered separate firearms. You just need a complete lower receiver to run them.
Also, sorry about the length and detail, little overloaded on caffeine and B-vitamins at the moment.