A shed on skids works very well.
A shed may seem too big for two but they will like it that way and it will let you add some more chickens later. It is also easier for people to use. And can be used as a shed if you ever take a break from having chickens or get a lot more chicken so build a bigger coop.
Climate matters. If you are in a hot climate, a screen house with roof and a few sheets of something solid on parts of two or three sides (around the roost area) to block wind-driven rain will be better than anything enclosed
If you are in a temperate to nearly semiartic climate then three solid sides and one open side work very well as long as it isn't too shallow or too deep (something in the neighborhood of 3 parts wide to 4 parts deep is good).
Use hardware cloth or metal lathe to cover any openings including open sides unless you have a run that is predator proof. Chicken wire keeps chickens in; it does not keep predators out.
Wide eaves are good.
If you build rather than buy, picking dimensions that use 4' and 8' a lot will save a lot of cutting and/or wasted materials.
If you use pop doors, set them up a foot or so to allow a lip to keep the bedding in.
A entryway so you can enter and close the door behind you before opening the door to the chickens is very nice. If that space is big enough, you can store feed and such there.
Poop boards under the roosts work well for many people. Chickens poop all night and don't move around much at night.