There actually is a list of all followers in-game. You can find it if you click the Garrison Icon next to your minimap and then select the "Followers" tab on the bottom of the window. The ones you haven't unlocked yet are greyed out but there is a description of how to get them (Achievement, Quest etc.).
The in-game list only shows the ones you can actually unlock since some are faction-locked. For a complete list I'd suggest looking at the Wowhead Follower Page.
While you can unlock every Follower that's listed in-game, you can only have 25 active at once. This requires you to have the barracks upgraded to level 3, otherwise it's only 20 active at a time.
Regarding your question about the optimal followers to send on a mission:
There are multiple things that influence the success chance of a mission. Your follower's special ability is by far the one with the greatest influence, but things like the level of your follower and the environment are also important and can lead to a higher success chance if countered correctly. If a follower has some special ability that's useful on a quest an Icon with said ability will show up next to him if you send him on a mission.