For a roost, I would recommend something at least 1.5 inches wide (that's how big "2 inch" lumber usually is when you buy it in the store.) Wider should be fine too, but I would not go skinnier than that.
People have done a few studies on what width of roost is preferred by chickens. Here is an example of such a study:
https://www.sciencedirect.com/science/article/abs/pii/0168159190900134
They found that hens preferred roosts 5cm (a bit under 2 inches) as compared with roosts 3.8cm and 2.5cm (that smallest one is about one inch).
So that means the hens were choosing the widest available roost, but does not tell whether or not they would choose an even wider one if it was offered.
(That study also found that chickens did not like to perch on a roost with a pointy top, like a triangle. Hmm, I might have thought that was obvious, but I suppose it's good to be sure.)
Depending on how big of a project you want this to be, they could try making a variety of roosts and observing which ones the chickens like better.
"Better" to a chicken might be wider or narrower, flat or rounded, rough or smooth, higher from the ground or lower, in a location with more shade or more sun or more ventilation or less wind, or quite a few other factors.