Congrats on the pistol permit and the purchase. A cheap .22 handgun is better than no handgun.
My wife and I submitted our application last month. If all goes well, we should have our permits sometime between December and March. At this point it doesn't matter too much because we just spent all of our handgun money on unexpected car repairs, so we may not be able to purchase anything until tax returns come anyway.
According to NY state law, only three types exist. Still, many counties will add restrictions (typically allowing you to carry target shooting or hunting, camping, etc). If you're caught carrying outside of these restrictions, they can and will take away your permit, making handgun ownership once again illegal.
It seems that many rural counties are fairly open to granting unrestricted carry permits; however, most urban and downstate counties restrict most permits, essentially making them a permit to own, rather than a permit to carry concealed.