Thanks for all the replies fellas - lots for me to think about.
The shed I have in mind is more like a little barn with boards on the walls (I guess you could say that of many sheds, but hopefully you get the picture) so leaving a gap top and just up from the bottom shouldn't be an issue, or maybe just a doorway with no door. Nothing will be kept in there except the bench, I think. (Again, I'm not clear what kit's needed but we'll find out).
As for type of welder, that's on hold - I'm planning on setting this up for my lad who (as Dave said above) is starting a wetalwork course next week, some time at home and some away and I want him to be able to practice while home - and teach me, of course. I've told him if he's going to be welding, he has to be the best welder he can be and from what I understand, that's all about practice. They'll be doing all types of welding and he's going to ask the tutors which type is best for practice - there's little point in me spending a few hundred £s just to discover it's not the type they'd recommend.
All that said, I know he ultimately wants to work on cars and we have one sat on the drive that I was going to pay someone to weld, using the repair panels some of you helped us cut. When he decided he wants to go down the metal/ welding route, it seemed fair to wait (the repair on the car's non-essential) til he can do it himself, hopefully next spring. Out of sight behind the rear bumper, it'll be a good first stab for him. To my 'understanding', MIG's good for that, and I'm really hoping the suggestion is we get one of those for practice, as I have lots of ideas for things to make of my own.