Local SIM. No sense paying $20/mo + 10/GB for what the Italian carriers will sell you for €10-15. If you buy it in the carrier's shop, you can sit there while it activates just in case you run into any issues.
"All the settings" on the tablet is setting the APN at worst, and if you're buying a SIM from the carrier itself (i.e. not an MVNO), your iPad will set the APN automagically. Ironically it likely won't do that with a Fi SIM.
Or just buy one of the UK SIMs off U.S. Amazon for $20ish and be done with it. Personally, I'd put my UK or Italian SIM in my phone and tether the tablet when necessary--that way you don't have to tear your hair out with T-Mobile's ultra-throttled data.