Don't make yourself crazy over choosing the bee types - yes, they are different, but they will ALL be novel and challenging to you. And queen bees don't last for a many years, either, (alas!) so it's not the same as, say, choosing a breed of dog.
Whatever you choose, try to get them from a local supplier of locally adapted bees, if at all possible. Many "local suppliers" are just bulk purchasers of southern bees, and merely middlemen between you and bee producers. I think this maybe more important even than type of bees, particularly in NY where winter is a challenge.
I am probably just prejudiced in this area because my three hives are swarms which just showed up on my farm - aka "mutt bees", so I have no investment in imagining their specific characteristics. OTOH, my mutt-girls are all still alive despite this fierce winter.
I second the suggestion to start with just ordinary Lang-style hives. (And I wouldn't make yourself too nuts over choosing between deeps + mediums, or all mediums for just two hives. Even if you started with double deep hive bodies with medium supers on top and decided to change to all mediums later, you could have the deeps cut down, or use them in other ways - nuc boxes, for instance.) I think the decision to use 8 or 10 frame is more critical (because the box widths are different so they won't easily stack on one another), though the frames in 8's and 10's are completely interchangeable.
I would also start with at least some foundation to give the bees a leg up in their first critical period. The queen can't lay, nor can the foragers stow nector or pollen until there are cells for them to do that. Even if you want to go foundationless eventually (and you can mix foundationless and frames in the same hive in the meantime) having some frames in the center of the boxes will offer your bees some ready-made cluster space (important if there is a cold period right after installation) and cell-building surfaces right from the start. You can eventually change out the foundations after you've built up a surplus of drawn comb (in a couple of seasons).
The only other thing that I strongly suggest to new or would be beekeepers who ask me what to buy is some form of a screened varroa monitoring/sticky-board frame. No matter what you hope or plan to do about varroa, understand that your bees will probably come with varroa, or will bring some into the hive almost at once. So you NEED to know what your mite levels are right from the git-go. By far the easiest way to determine this is with sticky board testing. It requires no beekeeping skills and doesn't disturb the bees in any way. I keep my bees on a solid bottom board with a screen bottom board above that under the hive body. This gives me a place for the sticky board, while still providing the hive environment of a solid board. Yes, it's an extra piece of equipment to buy, but I consider it an essential piece.
BTW, if you want expert, in-person advice about what to get have you considered making a day of it and driving up to Betterbee in Greenwich, NY? I'm sure they would send you a catalogue in advance so you could see what they offer. But they are very helpful to new beekeepers who are sorting out what they need.
I hope you have as much pleasure from your bees as I have had from mine this first year.
Also: one of the things which I found confusing about buying equipment was that the identical pieces might have different names depending on their intended use. A deep (or medium) box is just a size designation. You could have medium hive bodies (a common set-up) or deep supers (less-common, but sometimes used by commercial honey operations which have motorized hoists.) Planning to use deeps as hive bodies doesn't mean you'll need to lift them very often, nor will they likely be full of honey - which weighs a good deal more than combs being used for brood and bees, in any case. So don't let the 90-lb weight quotes scare you off using deeps as hive bodies just for that reason. And a 10-frame medium full of honey is not a powder-puff either!
Enj.