Pay full tax in MA. File MA taxes first, you will need the total tax payment to use as a credit against your CT taxes.

CT has a higher income tax rate than MA, so budget for the extra you are likely going to pay. Myself, I just take a few extra $ a week with my MA taxes, then use the "refund" from that to pay whatever I owe CT.

Do you rent? Once you move to MA, you will lose the ability to take the $3000 AGI deduction for rental payments off your MA taxes

Vehicle property taxes are more complicated and variable than MA auto excise tax. It is based on the current value of the vehicle as opposed to MA excise being a percentage of MSRP by age which stays static. They are typically due in July, billed by the town.