Generally for signage (actually many things involving a Pi), you want the entire OS to be read-only. No log files written, no cache, no disk maintenance. This way you can eliminate all wear on the SD and it can pretty much last forever and is 100% deterministic.
I do this for a few security systems and arcade-like public cabinets. I use OpenBSD mainly because I am more familiar with it. I blogged about it here if anyone is doing similar.
https://www.thamessoftware.co.uk/openbsd_readonly.html