Having used a variety of service provider, I think Vodafone probably has best overall coverage across the UK. Obviously, certain locations will be tricky for any service provider but they seem very good.
I've heard 3/Three are very city-centric and coverage really falls off outside larger towns and cities but I've not had one myself so I don't have first hand experience.
I would say if the service was such that you didn't get any because the phone was faulty or something like that, you could at the very least contact a newspaper like Guardian Money to fight your side if 3 don't refund you or cancel your contract.
2 bars out of 4 isn't so bad, it's when it gets down to 1 (or zero!) where reception is fuzzy. Obviously you want full signal but I've found in a lot of houses there are areas where mobile reception can be dodgy.