We make it sound really complicated don’t we? One of the many problems is that so many different things can work, so we all offer conflicting advice. It can be pretty simple but we can also make it really complicated.
I don’t know what your shed looks like but it is probably a good way to go. You need protection from predators and protection from the environment. For a lot of us protection from the environment doesn’t have to amount to much. A coop needs ventilation. A window to let in light can really help. You need someplace for them to roost and probably want nests in there. Add a way for them to get in and out and you are ready to go. If you could post some information about your shed some people might be able to give you ideas.
There are a lot of different ways to do a run too. I go with a predator proof coop to safely lock them in at night but a predator resistant run for daytime. Others want a predator proof run. For just 5 to 6 hens you may be able to find a dog kennel, chain link fencing, or something else on Craigslist. The uneven ground can be a problem but instead of burying the wire, which can be real work if the ground is rocky, you use an apron. Lay about 18” of wire flat outside the run (and coop if desired) and attach that to the bottom of the fence. You don’t have to bury it but a lot of people remove about 2” of dirt, the sod, and put that back on top to hold it down and keep it out of the way of lawn mowers and weed eaters. The idea is that the animal goes up to the fence, starts digging, hits the wire, and does not know to back up. It’s pretty effective.