I have given it some thought.

The primary concern is that whatever we post on Wikia becomes explicitly under a Creative Commons license (as opposed to no explicit license here, which probably implies standard copyright?). However, unless we have potential commercial interests in what we write here (eg. we might want to write a book using ideas we're using here), then this does not materially impact anything. The CC license still requires attribution, so in the extremely unlikely event that a third party decides to use any content we post, they will be required to give attribution and displace the CC license.

Public access is not a concern, as RPGuild is publicly accessible anyway. If any malicious editing occurs, then there is probably a history feature to revert unwanted changes (for a wiki site that big, I'd hope they have countermeasures for malicious editing).

The points Mutton raises indicates that a private wiki is impractical. Also note that there is no 'private' feature on Fandom.Wikia.

Looking at the wiki, having a wiki looks very aesthetically pleasing and organised. I'd definitely like to have a proper wiki, with info boxes and cross links and stuff like that.

In my considered opinion, I am okay with using Fandom Wikia, as Mutton has set up. If any individuals have any qualms about posting particular pieces of information, they can omit it from the wiki; possibly have a dummy page which provides an external URL to the character sheet on RPGuild so we can still find it.