Given your intended destinations you will be doing a number of day trips from your base. A car is probably more efficient, but not essential as all this locations have good bus connections to Perugia (but less so on weekends since bus transportation is designed primarily for commuters and students).
If you decide not to rent a car, then Perugia is probably the best option, being the region’s capital city and transportation hub.
If you opt for a car, which would be my choice, Assisi and Spello are centrally located to many destinations. With a car you might even consider some countryside accommodations, like agriturismo or similar. Just be aware that both Spello and Assisi have a ZTL, therefore cars are restricted in the historical center, therefore choose your accommodations judiciously so that you have parking available, if not at the hotel, at least in close proximity.
Regarding the time to travel I’d opt for late October rather than early November. The chance of rain will be slightly less and you will have longer days at least until the last Sunday of October, when Europe switches back from daylight savings to standard time.