conclusion was that you need to connect to the TV using an HDMI cable. The tv needs to support 1080p ideally, though you can select lower resolution of 720p. Something like this. Perhaps buy from somewhere that has a no-quibble returns policy, or test someone elses first, then buy exactly the same tv.
Seems there are still issues with some games though, which means resorting to a cable switch to reset the xbox. http://uk.gamespot.com/hitman-hd-trilogy/forum/tip-for-display-error-pal60-on-blood-money-29347769/. - this has a good tip for getting things to work.
Have a look aroind xbox forums for more info. Seems a common problem. If your current tv has an hdmi input, then may be worth trying with your existing tv, as it seems the xbox defaults to 50hz.
I do not have an xbox so can't confirm a particular tv works. Maybe post on xbox forums about a specific tv you are looking at to see if any users have the same tv and have it working in pal 60 mode.