I'm looking for the best combination of weather conditions, then airfare. I don't mind cold, but rain, I mind. Which would be better? Thanks in advance.

November is certainly cooler than October, you'll need a sweater and a light jacket.
An average of 4/6 rainy days must be considered.
So not bad weather, but sunset is at 5/5.30 PM.

I find Rome in October particularly fascinating. There is the so called OTTOBRATA ROMANA: the trees along the Tiber get wonderful colours for the foliage change. Same thing in the roman parks. Days get shorter, so in a sunny afternoon you get that particular light which gives Rome a wonderful golden colour. November is cooler and it can rain more but this year it has been a weir year, we have had a loooong and hot summer since May, so it is never good to give an exact weather forecast. Though, I can suggest October. Enjoy!

We visited Rome last October and the weather was perfect! It rained one of our days (but not for long). When you're in Rome...who cares!

Definitely October for warmer and drier weather. October is one of the best times of the year to be in Rome, weatherwise.
On the other hand, airfares are likely to be cheaper in November.

The hotel rates usually drop after Nov 1st. Regards, Walter