Traveling to Italy with 10 month old

Ok so my husband and I are traveling to Italy next year with our will be 18 month old. We are flying into rome and out of Rome. We want to take the italia rail to different cities in Italy- Venice, florence, Naples, and maybe some other places. I have so many questions but first, do I need a car seat if I'm taking the train? What are some good areas to stay in these diff cities? Should I bring a stroller or baby carrier or both?? Also any additional information would be helpful. We plan to use airbnb or vbro for places to stay