If you have a fan out of the room, make sure there is a way to get air into the room, preferably from the driest part of your shop (office with AC, etc.)
I have been in many shops, even sophisticated ones that build rooms or closets and don't think about air flow. A fan out of the room will just create negative pressure and no air flow if the room is tight.
On any kind of drying closet or room, have the fan in have a filter and be stronger than the fan out, that keeps dust from coming in the room so much by creating positive pressure.
Make sure your racks don't cause sliding in a screen to block all the air flow.
We make our drying closets for reclaimed screens out of electrical conduit and rubberized clothes line verticals and dry the screens vertically. Our drying racks for emulsion screens are wider than the screens and deeper as well and we put them in on two opposing corners, not along the sides. That allows air flow through the whole closet. We have box fans on top and a small heater and then a few pipes on the bottom to let air out that vent to the outside.
Hydrometer is essential You cannot tell the humidity of the room without it. Humans cannot tell the difference between 30% humidity and 60% in a screen room but screens can. I think a cheap one is fine.
We separate reclaim and the rest of the screen room and have a pass through closet. So the dirty and very wet side doesn't mess with the dry clean side. We have both AC and dehumidifiers. Sometimes if too humid you will freeze before you can lower the humidity enough with just AC.