This is just my 2 pence worth so take it for what is worth
I'm not going to recommend specific models or brands, but I have allways had good luck with Nokia, but others are good as well.
As for a website, check out
www.PrePaidGSM.net -- they have a huge amount of information.
I would get an unlocked phone, if possible (you can buy them cheaply on eBay). You can buy the phone and the service separately
I would do the pay as you go. The airtime does expire and the time varies with the provider. You will get a SIM card from the provider which stores the details of your phone number, etc. If you switch providers later, with an unlocked phone you just switch the SIM cards.
You may end up wanting multiple SIM cards: If you travel frequently (or for longer periods) to one country you may want to buy a local SIM card. For example, I am in Germany 3 times a year and so have a Deutsche Telekom SIM I use while there. Roaming is still very expensive -- your UK Provider will probably charge you an arm and leg to use the phone outside the UK.
There are also "International" SIMs -- these usually have better rates than roaming but not as good as a local SIM. That makes them good for countries you don't visit often. I have one from Lichtenstein (United Mobile) but there are a bunch based on the Isle of Man which have the advantage of a UK # (Lichtenstein is country code 423 and people allways say "What???" when I give them that number

)
Oh, and if you are traveling to US and Canada, we use different frequencies here. Ideally you would look for a "quad band" phone that handles the two NA and two rest of world frequencies, but these are more expensive. Tri band phones are more common but make sure your's has 900/1800 and one of 850/1900 rather than the other way around.
I hope this helps. Reply with any additional questions and I'll try and help.