It's the Vodafone 845 aka Vodafone Smart, and I've mostly used it on home wi-fi to be honest. I was surprised that it immediately allowed me to check my Google Mail without me getting a top-up - however my plan was not to use it primarily for "on the move" internet access, which can be costly on PAYG, but for voice and text (Asda PAYG SIM works fine, 6p per SMS, 10p/min to landlines and mobiles, compared with 12p and 20-50p using Orange etc PAYG to send SMS or call another mobile network).
Using it in the house for checking mail when not near a computer, some games, and the apps for Ebay, E-mail, etc. I will probably call Asda's customer service (staff working for Vodafone anyway) and see if I can get the details for using it for the web, just for times when I want something while away from the house... eg the mapping function, as Google Maps works with the in-built GPS (sat nav positioning).
Battery life seems a bit limited but then again I have bluetooth on, as well as a variety of background things running. I think Argos has it with 2 GB microSD memory card in the box, at 75 quid (+ tenner mandatory top-up). Possibly worth checking Vodafone coverage where you are, first, and then the 'Freebee' options to see if there's one with text + web access that may suit DS2.