Hi Meghan,
We typically mount our labels to either foam core or mat board. Wall panels are sent to a printer and are mounted to foam core. Smaller object and case labels are fabricated in-house and are mounted to mat board. If you are looking for durability, I recommend Sintra PVC board over foam core.
I've had luck (in climate controlled exhibition spaces) using painter's tape as a barrier between the wall and regular foam tape. Removable double-sided foam tape is ideal if you want to be able to remove a label cleanly from the wall. It is a less damaging alternative to regular foam tape. One side (label side) is high tack and one side (wall side) is low tack.
For temporary exhibits, a generous amount of painter's tape rolls applied to the back of a label sticks to a wall very well, removes easily without damage, and allows the label to be re-used by adding new tape rolls before re-application. This method is also a good way to play around with label placement before switching to permanent mounting solutions.
Command strips made of Velcro might be useful if you only need to shift the label a little bit. The velcro strip adhered to the back of the label would be re-usable for as a long as you need it, but you would need to replace either the hook or loop side depending on which was attached to the wall. You can also buy velcro tape on a roll, but I can't attest to the adhesive's strength over time to a wall or a label.
Hope this helps--I'm curious to hear what other people use!
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Melissa Krok-Horton
Collections and Exhibition Technician
Boston Athenaeum
Boston MA
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