I'm attempting to play The Secret World with my girlfriend. She will have no patience for soloing whatsoever, so I need to be in her group 100% of the time in order to keep her playing. How soon is a new character freed to group up, and what is the best way to do it?
When you create a character you will go through a short introduction level where you are escaping. This level is mainly designed to get you used to using skills and moving around the game world, but is instanced away from the rest of the game so during this time you cannot group.
Once you get past the introduction you are dropped near a town called Kingsmouth with your actual character - from this point onwards you're able to group, explore, do quests, etc.
It shouldn't take more than 15-20 minutes to do the introductory mission, and after completing this mission, most of the side quests and investigation quests through the rest of the game can be completed in a group - there are a few areas within the game that are designated as solo instances but these are clearly marked as you accept the quests and before entering the instances.
Entering these instances won't remove you from your party but you will be unable to enter them together. These instances are also optional (like every side quest in the game).
The main story missions for each faction are also solo, and cannot be completed in a group.
A full list of missions within The Secret World which cannot be completed in a group (ie: are solo only) can be found on The Secret World forums. Outside faction ranking missions and the main story, the number of missions with solo instances is probably less than twenty missions across the entire game.