I bet you'll love traveling light. For one thing, it won't take you forever to either find the garment you want in the suitcase (if you don't unpack fully at every stop) or get everything unpacked and hung up at each hotel (and then back in the suitcase prior to departure).
I think one of the most important tactics is to have layered outerwear. I prefer to have a warm layer (I use fleece; merino wool is also popular) and a separate waterproof layer. That's a lot more flexible that a lined jacket whose lining can't be used by itself. Since I don't travel during really cold months, I don't take a full-length coat. The last time I bought a rain jacket, I opted for a "Long" even though I'm 5'3"; it covers a bit more of my legs. I suspect a puffer jacket would be overkill in Italy in October, but if you have one that squishes down to nothing, I'd be tempted to use if rather than going out and buying a new garment. Something like a wool blazer would be warm enough, but those things are heavy, and they're a pain to carry around if you no longer need to wear them as the day warms up. On the first of my recent trips, I basically just shopped my closet. There were no disasters, but I did come home and buy a fleece jacket and a waterproof rain jacket. There's nothing like the experience on one trip to teach you what you can do better next time.
As for waterproof shoes, I think that's an individual decision. By the time October rolls around, the northern part of Italy could be getting cool and wet--not every day, but occasionally. If you get that combination, having cold, wet feet won't be fun. If the trip were ending in September, I'd not consider waterproof shoes necessary. October to me is a close call. I will say that I've run into the unpleasantly-cold-and-wet-combo several times: in Zagreb during the second week of October, north of Nice in May, in northern Andalucia the second week of April. I travel a lot, so there were definitely other cool and wet days; those were the ones I remember as being unpleasant.
I find having water-shedding slacks goes a long way toward keeping me reasonably comfortable. I'm talking about the 97% nylon things sold by PrAna, Eddie Bauer, Columbia and others. When I'm traveling in wet areas, I also take a pair of long johns (preferably merino wool). I find those, paired with the nylon slacks, keep me from getting totally soaked unless I'm caught in the rain for quite a long time.
