When you put in a new SIM card from a different provider, do you restore the phone afterwards from your backup?

I'm studying abroad in the UK, and I'm getting a UK SIM card for my iPhone so I can use it locally. I know that I'm supposed to back up my phone before I do the transfer, but then do I restore it right after or not until I put the old SIM card back in? And can you still plug the phone into iTunes and download new apps and music while you have a different carrier?