Just started cycling myself (although my employer not in the cycle to work scheme unfortunately!!).
Anyway, himself got a bike also for same reason and he is over 6 ft.
We went to a large bike place and the staff there were very helpful in terms of what we wanted.
They recommended hybrids as a 'lifestyle' bike, basically a hybrid is a cross between a racer and a mountain bike, the bike wheels are larger than mountain bikes meaning you cover more distance for less effort than with a mountain bike and because you dont specifically want speed theyd be less fast than racers. Theyre kind of big and comfy. I alread knew going in it was a hybrid I was after.
The correct frame and saddle height for you should mean that when you are seated on the saddle you should be able to put one foot to the ground - on your toes, not flat. Also when pedaling your leg should not go into full extension, ie, there should be a small bend in your knee when your leg is as extended as it can be while you pedal.
Himself got an extra large frame, but the only way to know what suits is to take it for a test ride and get the bike shop people to change things (I got them to change the saddle a couple of times and move the handlebars until I was comfortable).
A make to try out is a Giant, thats what I got, and himself was about to get one but changed his mind after pedaling a few different ones around.