I'm not familiar with Troop A specifically, but most NYSP troops primarily operate on county dispatch, so you might not get anything. If they do use their VHF frequency, (assuming you're in Chautauqua County) you only need to program Zone 3 mobiles--you'll only be hearing a mobile if it's within a mile or two of you, so you won't hear anything on Zone 1, 2, and 4.
As for Troop T, Car to Car will likewise only be audible if you're close to the Thruway. Troop T units are dispatched by the Thruway Authority on Thruway Ch. 3 and 4. You'll probably want to program both Channel 3 and 4--both carry the same traffic, just from different sites--and see which has the best reception (although I scan both, as on occasion one will be down for maintenance).
Thruway Ch. 3: 453.425, 123.0 PL
Thruway Ch. 4: 453.525, 123.0 PL