I've done both. I started with a prefab, because I didn't have a clue how to start building one, and I needed it asap. I ordered mine from my pet chicken, and in general, I like it. It seems to be better quality than some of the ones I've read about here. It was fine for my 2 hens, but when I added a 3rd, there was "technically" room, but they didn't like it. (that's your first clue, the chickens decide!) I had the prefab up for a year and a half, and it did fine. Did have to add screws and fender washers to reinforce the tiny staples they used on the hardware cloth, and more secure fasteners, (because I'm paranoid about raccoons) Waaaay too small of a run, but even the company stresses that it is not intended for full time confinement. Aggie the EE says no time confinement! That was ok, the girls had a yard to exercise in. Bending to clean the pull out tray was easy, but hard on my old back.
So, with no building experience and few tools, I built my next coop. Still small, but bigger than the prefab and the girls are happy together now. I had a hand saw, screwdriver and battery run drill, and that's it. No plan, other than one in my head. It took a couple months to do, and I had to redo things more than once, but at least I knew what worked and what didn't from having the prefab, and in general, I'm quite pleased with my work. It's sturdy and safe and if I can do it, you can too. I still have the prefab though, and it's in very good shape. It's going to be used as a quarantine and safe introduction coop.
For your three, you could do a prefab, if you are really unsure of your ability to build. I would say though that a prefab shed is always a better route, if you can swing it. Bigger is better in all cases, and you'll really like being able to walk in.