Leti, this subject has been extensively discussed on the packing forum so I'd suggest spending some time browsing through the threads there.
https://community.ricksteves.com/travel-forum/packing
The carryon-only method works for some but not for others so it comes down to what works for you. In either case it boils down to luggage no bigger or heavier than you can easily manage by yourself. For most of us, traveling in Italy involves being able to carry our bags up and down flights of stairs (sometimes long ones), in and out of trains, and drag them across stretches of cobblestones and other problematic pavements. The less you have to haul, the less of a headache this will be. Topline tips:
• Wardrobe should be mix-and-match: all tops should go with all bottoms. Don't pack by individual "outfit".
• Fabrics should be easy-care; nothing fussy. Lightweight is advised for Italy in the summer, and dark bottoms don't show dirt/stains.
• Plan on doing laundry. Lightweight shirts, pants, etc. can be rinsed out in the sink and drip-dried overnight, and hit a self-serve laundry partway though the trip. Some travelers pay to have their laundry done but we've preferred to do our own.
• Keep accessories to a minimum. I bring no jewelry and wear the same pair of gold earrings the entire trip. A lightweight scarf can dress up a plain shirt, if desired.
• 2 pairs of shoes only, both well broken in and sturdy enough to walk in all day. Wear one; pack one.
• share toiletries when possible, and just buy in Italy what you run out of.
My husband and I routinely travel in Europe and the U.S. for 3 weeks at a time and both check a 24" suitcase (plus carryons) BUT they're not packed to excess. They're heavier at the end of the trip because of items we pick up along the way but we're careful not to bring anything at all that won't be worn multiple times or will be difficult to care for, such as white pants. No one is going to know or care if you've worn the same sink-washed shirt 3-4 times in one week! :O)