Check or carry the way you normally would for any other trip, assuming you've flown before. I check bags. No way I'm lugging two suitcases and a car seat around. There are never any guarantees with bags, so just keep essentials in a carry on - things like medication, ID, valuables, electronics, etc.

Pre and GE have nothing to do with Italian immigration. Unless you have an EU passport, you'll go in the line that every other foreigner uses. It's generally not a huge deal - queues for CBP in the US back up way more than they ever would in Italy, in my experience. It's basically standing in line to get to a window for a passport check, then you go to regular baggage claim and get your luggage, and customs is walk-through without any forms or much interaction unless you have something to declare. Foreigners use the non-EU lane, while EU citizens use the EU lane, usually just a walk through the same area with a rope in the middle. My experience is that on a foreign passport nobody asks you anything since you're probably not returning home (where customs declaration is important), while on an EU passport a customs agent will say hello to me 50% of the time. Do declare anything that you need to, but assuming you're not required to like most tourists with just their luggage, answer any questions if someone stops you.