Would definitely second local, hunker, but local ones do deliver over quite a wide area. To answer your questions:
Which company delivers it? Not that I suspect it will be any good to you (!) but Bee-Organic
Which are box-friendly fruits/veggies? The website tells you ahead of time what you'll get - here's next week's. We don't get fruit, as the farms round here don't necessarily grow fruit, so some can be imported, etc. We do have a fab soft fruit farm which has a shop quite near, so that is our alternative.
Which are less good? Most things are fine - just use them in order of most-least perishable
Anything to avoid utterly? Things you really don't like. I try to convince myself I'll eat cauliflower/sprouts, but it never happens, so I've asked for them to be off my lists (and you can take your dark looks away, Franny).
And is there a meat/cheese/eggs/milk option as well? Not in ours, but plenty of places will deliver those things, so can set it up differently.
Do you feel it offers value for money and do you eat things you wouldn't normally buy now, because you have to, because it's In Your Kitchen? Yes, absolutely. I'd recommend getting cookbooks which specialise in seasonal veg (I am really enjoying using this at the moment), but it is fun, because you can't stick to the same repertoire all the time, and have to be inventive. I'd recommend it. You can always try a couple and find the one you like best.