Train would be my recommendation; they are reliable and comfortable, and you do not need to worry about routing and parking, nor do you need to bring and carry around a car seat for the baby. But with luggage, it would be much easier if you plan to “wear” the child (in a front or back carrier, as appropriate) while traveling. If you want to include a stroller in your luggage for use at times, that is up to you. I raised and traveled with my children, and then they raised and traveled with theirs, without ever schlepping around a stroller (even if they used one at home). My older son and his wife took their firstborn to Ireland for 2 weeks when the baby was 9 months, all with the boy in a Baby Bjorn carrier. They have lots of great photos of a smiling baby making friends with people there. My younger son and his wife stayed closer to home for the first year, but we had a great time camping and hiking together when the twins were 11 months old. The parents each wore a baby on the front, with the daypack full of baby needs on their back.
But the logistics of baby equipment will be up to you. I will move on to suggestions for train travel ( or train plus boat, which works well for this journey.
Our favorite way to reach Italy is to fly into Zurich, and travel south via Luzern and the scenic Gotthard Pass route over a period of several days. Prior to last August, one had to plan carefully to ride a train over the pass instead of the usual route through a deep tunnel. But an accidental derailment closed that tunnel to passenger trains, and currently it is scheduled to be closed for repairs until September 2024. So it may or may not be open for your visit, but if not that just makes taking the scenic route easier.
You don’t say where on Lake Como you plan to stay, but my suggestion works for anywhere on the lake. It is based on what we did this past September, traveling with adult kids and two grandchildren—the twins who are now 11, and happy travelers.
From you landing in Zurich, take the train straight to Luzern. This may or may not be a direct train; the usual schedule has been changed by construction, but even with a change at Zurich Hauptbahnhof it is an easy journey of about an hour. Spend 2 nights, either in Luzern or ( what we did) take. Lake boat to the nearby town of Weggis and stay in a sweet little family run lakefront hotel, with a lakeside restaurant and access to a swimming pool.
https://www.gotthard-weggis.ch/
From here to Milan, you could either return to Luzern to catch the train, or do as we did and ride a lake boat from Weggis south to Flüelen, where we picked up the train to Milan. Everyone in our family loved the boat ride, S well as the scenic train.
From Milan it is an hour’s journey to Varenna, if that if your choice. For Bellagio, you take boat the short distance from Varenna. Or you could leave the train at Como San Giovanni, before reaching Milan, and travel by ferry to your Lake Como base. It’s all good. . .
