I would start with the simple majority veto override states with term limits where the governor also does not get to pick their LG, so AL, AR, TN, and WV. Then would come KY and IN, which also have simple majority veto override and term limits, but the governor at least gets to pick their LG and KY has some pretty strong executive order powers.
Next would probably be VA, where the governor does get to veto with a 2/3rds override (including line item veto), but they can't run for reelection, can be stuck with a separately elected opposition party LG, and don't get any formal say in judicial appointments.
For strongest, FL certainly comes to mind with essentially unilateral judicial appointments, 2/3rds veto override, choosing your own LG, and pretty strong emergency powers invoked almost yearly with the frequency of hurricanes there.
Although the Governor of Tennessee always seems to be popular when in office.
