You will have to have Highway use tax credentials as well at least for New York State. Check with the other states you plan to travel in. Save your time and money and apply directly to NYS and other tax department offices.
Department of Taxation and Finance
Between the application and sticker you will have close to 20 bucks into it.
Any vehicle with a Gross or max rated weight over 18,000 lbs. must have a sticker. Its an expensive fine and they will suspend your plates if you don't apply, file, and pay if taxes are due. They can ground you and pound your truck if you get caught with no sticker as well.
You will have to file quarterly all miles driven in N.Y.S.
Even if you don't travel in N.Y.S. you have to file. You don't have to pay if you don't drive in N.Y.
NYS thruway miles are exempt but the state will whack you with the tolls. Its not a big deal just a hassle to do.
Shoot me a PM if you need help with it.