Hi @mrgibons
You can add a user field type in your Characters CPT and set it automatically when a character is created. To do it, you can use acf/save_post hook.
To list the character of a current user, you can query it based on the user field type. This page should give you more idea about it: http://www.advancedcustomfields.com/resources/query-posts-custom-fields/.
I hope this helps.
