Pittsburgh to Italy via UK

I think either way will work. Whatever you do you want to at least book a multi-centre flight US-UK and Italy-US as one ticket. Whether you add the UK-Italy leg on as well or book it separately depends on pricing and the convenience of flight timings.

If you want to fly to Florence what I would very seriously consider is booking the BA flight from London City airport (LCY). LCY is by some distance the best London airport to transit through. It's close to the city centre, easily accessible by public transport and the cut-off time for passing through security if you have just carry on is just 20 minutes. The planes are small so you need to check the rules on carry on bags.

You should be able to book the whole trip Pittsburgh - London - Florence - Pittsburgh as one ticket with either AA or BA.

You need to get yourself an ETA to enter the UK (assuming you are a US citizen) and will also need to pass through the EES system entering Italy. You may also need an ETIAS to enter Schengen - it should be introduced this Autumn but is likely to be delayed.

amazing, in the time it took me to log in John's post appeared saying pretty much what I would have said about the various passport control processes.

Summary: how you buy the tickets won't affect it. You need to apply for the UK ETA before you travel (but not too early because it's valid for 2 years so might be useful on another trip) , you will pass through the Schengen EES process when you arrive and depart Italy, you need to check back early next year in case ETIAS has finally been implemented on top of EES.

When comparing ticket prices bear in mind Easyjet/Ryanair extra costs on top of actual fare plus the costs of reaching their London airports, if the London City option is viable the cost of reaching it will be less so you have more leeway with the fare.

If you are going straight home from Tuscany, I would book a multi-city flight so you fly into London and fly home from Florence/Rome, and then just separately book a low cost flight from London to an airport near where you need to be in Tuscany. Low cost flights from London to Florence aren't that common as it's a small airport- but you'll find low cost flights to Pisa which is nearby (not sure how close that is to where you need to be). And of course plenty of flights to Rome. Depending on where you are staying in London it's very straightforward to get to Gatwick, Luton, or Stansted. Low cost carriers don't operate from London City or Heathrow.

Cat makes good points but I would not automatically rule out LCY. Firstly if you look to put everything on one ticket you may well find options using LCY that are competitive with booking the long haul flights on one ticket and a separate UK to Italy flight. You are quite likely to get a routing through LCY if you request Florence as both airports have short runways so can only be served by smaller planes. So BA have their flights to Florence from LCY rather than using up precious landing slots for smaller planes at LHR.

Secondly, whilst there are no "low cost" airlines that use LCY it doesn't mean that you can't find keenly priced flights from there. Admittedly we use LCY often because we usually check bags and BA offer them for free so comparing with the likes of EasyJet and Ryanair becomes a lot closer. But for me, the bottom line is that LCY is so much better to use that I am willing to pay a bit more.

Finally Cat is right that if you stay in the west of the city LCY is a bit further to get to, but then I would recommend staying more centrally anyway.