First off, welcome to the site. You'll find a lot of good folks here that are willing to help out and share all the advice that you can handle.

Second, sounds like you have a great relationship with your dad and that you shared some really great memories with him when you were younger. Be thankful for that (sounds like you are) because it is something that not everyone has.
As for your situation...I'm not from NY and know nothing about it, but many of the members here are so you'll get lots of good advice from them. That said, your best resource is probably still going to be your dad. If he is an outdoorsman, he'll have buddies that are outdoorsmen too and maybe he can set you up with one of them to go with or at least talk to. Trust your old man.
As for equipment I suggest that you find a good pro shop and let them set you up. There are a lot of great options out here for just about every budget and most will work hard to get you the right equipment at a price that you're willing to pay. Be careful because it is VERY easy to go over your budget in a hurry.
There are several good magazines that you could turn to and Deer and Deer Hunting is my personal favorite. Read carefully and you can gain a lot of valuable information from the stories written in them.
Lastly, practice, practice, practice.
Best of luck to you in your new adventure and remember, listen to pops.
P.S. Once you do head down this road be sure to take those stories back to your dad and share them with him. It will mean a great deal to him and probably make him feel like he is there with you.