TL;DR - You need to ask an accountant.
Depending on the company you're doing work for in the US you might need more than just a way of paying by credit card. Some companies will want you to have an EIN (Employer Identification Number), which in turn means you need to get an ITIN (forget what that stands for - basically it's a Social Security Number for people who don't normally get SSNs - like non-US folk - so all the tedious admin stuff carries on working :-) Google will help you find out more. The process is fairly painless - but does take time.
Not all companies require this - and it's certainly possible legally for companies to pay you without these if the project is set up the right way - but some folk in the larger companies require 'em, or work in a way that requires 'em.
My US experiences also differ from Gary E's in that:
Some US companies are more than happy to do wire transfers. Depending on how their accounting processes are set up they may actually prefer it (paying for "people time" on credit card's being seen as a no-no by some firms). Many larger US companies have EU branches anyway and may prefer it.
I've never had a problem with PayPal that's due to the company not having a PayPal account (you don't need one - you can just pay with a credit card directly). I have had problems because it's seen as unprofessional, or because they prefer to pay another way (direct bank transfer, money transfer, cheque).
Setting up a Ltd. company in the US from outside the US is, unfortunately, a complete PITA unless you're there physically for a while to setup bank accounts etc. I'd try and avoid it if possible. I have been told that it can be more tax efficient though - but you'll need to ask an accountant.
Some companies in the UK will want you to be a Limited Company. Not because you have to be legally, but because it reduces their risks (simplifying slightly - if you muck up your taxes as a sole trader they might be responsible for paying some of those taxes, if you're a limited company they won't be).
Setting up a Limited company in the UK from somewhere else in the EU is pretty painless, or at least so I've been told. Best ask your accountant on the details though. Probably best to wait to see if it will be an issue for the clients you work with first.