Purchasing unlocked UK IphoneSE using in US long term
I will be purchasing an IPhone SE in the UK while there for an extended stay. I will then be needing to use it on a permanent basis in the US. I split between both places. Is it better to buy an unlocked IPhone at the Apple store or will there be difficulties using it if purchased elsewhere? I've read GiffGaff have good truly unlocked prices and reliability. Here are the specs on GffGaff
https://www.giffgaff.com/apple/apple-iphone-se/phone-details#specification
I realize I can get a Sim card in the USA, I have read that any sim card will work in an unlocked IPhone. But, I am unclear on what that means in terms of this list on the Apple site. Am I understanding correctly that this means if I want to have get a monthly plan in the US with a sim card that I need to think in terms of what Network to use with what model number? Why do some sites say a sim card will work in an Unlocked IPhone but then this Apple lists only certain providers work with certain serial numbers etc?
http://www.apple.com/iphone/LTE/
I have also read that the first time an iPhone is used it locks onto whatever network you use the first time. Is that true with an unlocked IPhone and is that something that can be switched at the Genius bar in either country when a local sim card is swapped. I would be grateful for the latest information on how to smoothly transition between both countries and how easy it would be to swap Sim cards when needed.
Many thanks.
MacBook, Mac OS X (10.7.5)