I bought a couple of BunnyBusiness metal runs (advantages - can fold flat to store, no rotting like wood can, nice height so I can put a box inside and the pigs are protected from predators) I peg ours down with heavy duty tent pegs.
I got a 2nd hand rabbit hutch , got DH to strengthen the wire, cut a dor in the end and secured it to the run with hooks and padlocks.
It is a blooming pain to move it all every 4-7 days depending on how they destroy the grass 
but my Himmy loved the shade.
I had a small wooden hut inside the big run , the hutch attached to the smaller run.
The rabbit hutch has been in the Pighouse for the last year and even under cover the quality isn;t great (its a well known PetStore Chain) .
You might be better with a seperate indoor cage ecause there will be days they can go out a while but you won't want them out all the time. I don't let mine 'choose' when they go out - partly because the grass needs to be dry and partly because they need to be safe from predators. I don't leave mine alone unless its 30 minutes and my NDN are out in their gardens to deter foxes and cars .
Best thing for outside is a shed or playhouse - look on Pinterest fr ideas on rabbit houses and adapt. It is so much nicer cleaning the cages and chatting to them in a shed. You can have hutches+floor space.
Needs to be ventilated, they get warm.
You could attach a run (but you wouldn't be able to move it about which is the big advantage of metal runs)