Personally I recommend Vodafone. They're not the cheapest, but they have the most robust coverage nationally (of course all the networks have some specific geographic coverage issues, though I've experienced the fewest problems on Vodafone). Vodafone's population coverage is at 99.7%, and their use of 900MHz GSM, as opposed to 1800MHz GSM like Orange and T-Mobile, means their signal goes further and reaches inside buildings better.
O2 is a popular choice with students, however, because it's pretty cheap. Again it uses 900MHz GSM. O2 doesn't make me feel particularly warm and fuzzy inside, but I wouldn't beat you up with a fire extinguisher if you decided to go with them.
T-Mobile have Web n Walk, the best mobile data package by far in the UK. They also have pretty variable coverage compared to Vodafone, but it's ok. Orange, well, you get good value if you want free landline broadband - but you need a premises with a BT line installed to get that. Neither of these networks are probably your best choice for your requirement.
I wouldn't worry about 3G too much to be honest. 3G services are still quite expensive here and you'll trade handset size and battery life for stuff you probably wont use - unless it's mobile data you specifically need.
I've neglected to mention Three. They're the smallest and worst network in the UK by a long shot. Their value perspective has recently been eclipsed by the other networks if you shop around for a good deal, all their front line customer services are manned by a very generic outsourcing company in India (I've dealt with some fantastic Indian outsourced CS operations, 3's never has been and probably never will be one of them) and I still have reservations about the technical quality of calls on their network when compared with the general excellence Vodafone offer.
You could do much worse than a mid-range Nokia handset on Vodafone Pay as you Go.
I hope my mumblings can help you in some way or another. If you do specifically want 3G capability then you'll probably inspire some lively debate at
www.talk3g.co.uk
I hope you like the UK! Pack a brolly!
