It's difficult to discern. For the most part, your best choice is the group that you feel works best with your demeanor and outlook. Homura-san's organization looks only for skilled fighters, wheras Arts and Crafts and Cooking will accept anyone who has something to offer and does not want to travel the halls alone, be they a strong warrior, a brilliant mind, or possessing of some other skill that we can implement into one of our teams. Cooking has a greater focus on acquiring things within the institute, from the clues the radio gives at night to the creation of weaponry, while Arts and Crafts has a greater focus on exploration. History Club is relatively new, three or four days old at this point, and I do not know the entirety of their objectives. You would be best asking them.

Your best option is to choose an organization and try running with them for a night. See if you like the organization, and if you don't, look to one of the other groups. We all work together, it is mostly just the leadership styles that differ.