Debian packages and/or RPMs are fine. If you want to get fancy and put yourself in package repositories, you may get more casual users discovering the software, but, IMNSHO, that's certainly an optional bonus goal for an application like Fantasy Grounds.
A more "technically correct" location would be in /usr/local/share, but [/opt] is another totally valid choice for large, self-contained applications that are less integrated into the OS, for example, Fantasy Grounds. ;)
TL;DR: I'd strongly recommend your root install folder be /opt/FantasyGrounds.
(And yeah, you could stick a SmiteWorks company folder in there if you wanted to or needed to for some reason, but it's not really a Linux standard and a bit overkill for me in this case.)
Assuming you go with something like /opt/FantasyGrounds as your root install directory, you can make setting up that directory (and setting the permissions on it) part of the package file. The installed will use a UI to ask for elevated permissions to do the install in a friendly way, and then you're set. That is, if you make the package install process allow the installing user (and maybe the "all users" group) to write to the install directory to start with, you shouldn't have to worry about elevating permissions.
If you have any trouble sorting this stuff out, I'd be happy to help. I've not done tons of packaging specifically, but I know enough (and I have half a dozen folks at work who are masters at it) that I can probably help with any hiccups faster than folks with only some experience.
Thanks again for the support!