Any phone powered by Android will do what you’re after. There are loads of apps in the Android Market that do GPS logging, ride maps, all that jazz. I currently use MapMyRide, but Google’s own MyTracks is also very handy. MapMyRide links to facebook so I think you can be tracked live on that or maybe on the MapMyRide website? MyTracks just logs your position & speed by GPS and gives you a rundown of everything but no live tracking.
As far as the actual phone goes, your best bet would be to go and have a word in Carphone Whorehouse and see which network & tariff will be cheapest for you while abroad.
I’m currently on a Sony Ericsson Xperia X10 on O2. Initially thought it was a bit rubbish due to naff support from SE and O2, but I’m now running a homebrew (non-SE/O2) version of Android and it’s phenomenal. Bit old now though, and the new Sony Ericsson Play (Playstation phone) is due out soon.