A run is easy to build - even my DH managed it. He used sawn timber and chicken wire, but weld mesh would be good too.
We eventually took it down though, because it was fixed and the garden suffered a lot underneath it (mostly because I got carried away with the number of chickens we have).
If you're planning a run for 2 or 3 birds, I'd make it a moveable, roomy one with a way of hooking it to the chook house so they can't come apart because if there's a gap, the girls will try and explore it.
For a chook house, most things would do. A converted dog kennel, if it's 2 birds I think even a guinea pig hutch would do the job. As long as you can put a roosting pole in the sleeping area (a smooth piece of timber with rounded edges and a flat top - ideally 2/3 inches across the top).
My girls mostly lay in big flower pots filled with straw in their shed, although about 4 of them favour the old guinea pig hutch that's there.
They haven't damage any plants yet, although their feet have done a bit of trampling and kicking. The damage is balanced by the entertainment they give.
Our garden would be so, so dull if the girls weren't there. Oh yes, and they've eaten all the black and greenfly and slugs and snails. Our hostas and beans are fabulous!