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I'm quite happy with the service I get from Nationwide. Not the best deal on interest rate, but their internet banking works, it's Visa, and I've purchased in many countries and online with it no problem. Never had horrible charges out of the blue, everything is well documented.
Maybe consider Natwest as well, I've heard more or less positive things about them, but not used their online banking.
To clarify, I mean a relatively easy user interface so I can track the spendz. Also, wider acceptance might be useful.
AMEX are tempting as the BA tie ins look good but anywhere I've worked in retail/service (at least in the UK), didn't accept AMEX
I'd like to avoid booking another flight to Colorado and Hotels on my debit card, if at all possible.