Digital camcorders

With the imminent arrival of my first child I’ll be getting a camcorder so that the Grandma’s won’t be starved of seeing their newest grandchild.
Several things I need to address:
I live in Canada and the folks are in the UK;
I’d like to buy a DVD as opposed to a VHS camera;
I’d want to get a camera that records onto DVD so that I could send said DVD out to the folks without any conversion or mucking about,if such a machine exists.
Not too much to ask!!
So over to you guys for your expert advice please.