1) it's always good to keep your domains with a separate company to your hosting. so buy your domain name that you want.
2) Buy hosting - linux hosting will be just the job for IPB and most things. Check OCHostreview. Before you buy, though, phone them and say you want to deploy invision power board and will they install it for free (after you have bought the code from IPB that is) if you sign up with them (if you don't want to get involved ftp/mysql/permissions setups).
I use Vidahost (their start account will be just fine for you), but there are others that are recommended on here: TSOhost and register1 - checkout Ochostreview and makeup your own mind. Don't get american hosting though - your Google UK ranking will be compromised.
3) change nameservers on your domain name to point to your hosting and you're done! have fun with IPB and let us know if you have any probs.
/ that's an honest opinion