October would be better than September, less heat and fewer tourists - lots of tourists but not as many as September.
I'm going to Poland and Hungary in September, before the cold weather sets in. If you haven't been to Italy, I urge you to put it at the top of your list. I think everyone should visit Italy. October would be better than September, less heat and fewer tourists - lots of tourists but not as many as September. The classic trip is to fly into Venice, then see Florence and finish in Rome. If you have 2 weeks on the ground, you could add another stop and some day trips. If you have 3 weeks, you could add the Amalfi Coast. If you can fly home from Naples, you could fit the AC into a 2-week trip without rushing.