Yup, most are provider independent.

Low usage == PAYG.

Minutes expire after NN months, where NN is typically 6 or 12. Put money in and the clock resets.

Each provider has a different pricing scheme (day of week, time of day, maybe usage). I used Virgin Mobile because it was the simplest, and they're everywhere.

Use outside of UK, esp U.S. of A. == Get an unlocked TRI (or QUAD)-BAND phone. Unlocked means it can be used on any GSM provider. Tri (or quad) band means it works on three (or four) frequency bands, and the US, in particular, uses frequencies not used in UK or Europe. I bought an Ericsson T-39 18 months ago, and it's been fine in the US, UK and Europe.

With some PAYG providers, you cannot roam with their SIM chip in the US. You will need a US provider SIM chip (which will be a lot cheaper anyhow). I've bought T-Mobile SIM chips on e-bay. Far less expensive than buying at a T-mobile store.

Charges: Unlike much of the rest of the world, all calls are charged for in the US (i.e., incoming as well as outgoing). Advantage? Someone calling your mobile phone from abroad doesn't get gouged outrageous cell phone charges the way we do when we call someone's mobile phone from the US to Europe.