Depending on the zone you have to take more ore less effort to make it safe. Put all electronics and motors outside the cabinet. It is not difficult to to seal the hole for the shaft of a lead screw. I am not sure about limit switches but to be sure, they can be activated by a sealed shaft and placed outside the cabinet.Those two solvents also mean that the entire apparatus is going to be explosion proof, which I'm sure won't make sourcing motors or a PLC easy. But that's a problem for another day.
A polished steel lead screw running in a bronze nut could do without lubrication. Covering the lead screw won't hurt. You could construct in a way the lead screws are fully covered by the table. A lead screw is easier to clean/maintain than a ball screw.Given some of the solvents we use, I'm hesitant to go with a ball screw, simply because I'm not sure how well internal lubrication will hold up
There probably is a formula but your demands aren't high. I would go for a 20 mm lead screw. My small lathe has one and its length is about 40". It can handle a lot of load and still is accurate (0.02 mm)First, is there a reliable formula for determining minimum screw diameter to move a given mass?