You need an EZ Pass transponder, from whatever state in the consortium you prefer. One or two states call it something different (Illinois calls their version the i-Pass, I believe), but any EZ Pass transponder will work in any state that's a member of the group.
Ohio:
ezpassoh.comNew York:
e-zpassny.comEZ Pass Group:
e-zpassiag.com (which does not directly offer transponders, etc. to the public, but has some information and links)
It may well be worthwhile to compare the fees for various states. Some charge maintenance fees, some do not; some have fees or deposits for transponders; and some offer discounts for in-state tolls or other perks.
If you'll be traveling along the NY thruway somewhat frequently, I would suggest considering the New York one with the motorhome plan, which charges you car rates rather than motorhome rates (and saves about half the toll costs, at least for the case of one without a toad).