I've got 2 American T-Mobile sims so I sort of know how this works.
1) Phones:
Your phone needs to be at least Tri-Band to work in the USA GSM networks (it will not work on a CDMA network as this is totally incompatible) but this does not mean that your phone will take an American SIM, just that with a SIM it can handle, it would work in the USA.
Ok, assuming that your phone is Tri-Band, it also neds to be unlocked. As I'm sure you know, putting a Vodafone SIM in an O2 phone in the UK usually doesn't work. Well the same thing applies here.
So, you need an unlocked phone that is Tri-Band. A Jailbroken (Edit: and unlocked with something like redsn0w) iPhone would fit the bill nicely.
2) Networks.
As I mentioned before, you need to make sure it is a GSM network not a CDMA one if you want to use your own phone. CDMA is an alternate network that is incompatible with GSM and is sold in
Walmart as well as GSM phones. T-Mobile and Verizon are GSM, Net10 is CDMA (I think, don't hold me to it).
3) Numbers.
In the USA, given the scarcity of phone numbers, your phone must show activity at least once in every 90 days (maximum, some operators use a tiered system. 30 active for a $10 top up, 60 days for a $30, etc.) or the number is re-allocated and you have to re-activate the phone from scratch. I keep mine going by simply adding a $10 top up every 3 months (T-Mobile was the best for this only needing $10 for 90 days). Given how often I'm in the USA, that's worth it for me (Also, I love being able to say I have an orlando 407 number

). If you don't need to keep your numbers after the trip then it's not an issue, but it's worth bearing in mind.
4) Use in the UK.
As far as I can tell no USA PayG SIM works in the UK. I dropped mine in my phone here (which is fully unlocked) and no dice and after some research that is the way of it for all of them. Again no biggy but worth noting.
5) SIM vs Phone
Usually you find that buying a package deal (especially with the cheaper operators like Net10) is as cheap or cheaper than just a SIM as they always throw in minutes or other incentives. Even though I used the SIM in my UK phone, I bought a package with a cheap Nokia as it worked out a better deal.
Summary
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I went GSM as I wanted to put the SIM in my iPhone and use all of the funky apps such as the WDW park maps but assuming you don't care if you have to re-activate them and get a new number, and assuming that you only want to make calls then I'd just grab the cheapest package phone on the shelf in Walmart.
The only reasons not to are:
You want to keep the number (in which case you don't want the cheapest, but the easiest to top up from the UK and the one with the longest time before de-activation).
You want to use your own phone.
Phew! that was a long one! Hope it was of some help.