I am also planning my holiday to Montepulciano this summer since it was cancelled last summer due to covid. I have stayed a few times in Montepulciano and it's one of my goto places when I am looking to get away from the larger cities. Montepulciano has come a long way with public transport since I started visiting many years ago. If you need a driver or taxi service, here is the official link to transport options: https://www.montepulcianoliving.it/it/trasporti/.
If you are looking to stay in town, I highly suggest Alberto 57, one of the apartments by Charming Homes (https://www.charminghomemontepulciano.com/en/alberto57.html). I've stayed here a few times and it's spacious, clean, and Alberto, the host, is wonderful.
If you are still open to a place outside of town, there is no better place than Fonte Martino bed and breakfast (https://www.fontemartino.com/). It's 5-minutes outside of town with beautiful view of town. The rooms are spacious, modern, and the hosts David and Toby are amazing. I stayed here in summer 2019 and this is where I will be staying this coming July.
Best of luck with your planning! -Norman