Crossfit. I know as much as someone would want to know. Have fun with it, it can be a great way to get in shape. Your wife is right, it can be cult like. As long as you understand and take responsibility for your own ability to regress or progress (make easier or harder) the WOD (Workout Of the Day), you shouldn't suffer any of the common injuries associated. Maybe not my first choice for someone to begin an exercise program but in gym memberships, convenience will always trump other considerations except maybe price.

One of my workouts during the day, (I set aside 2-3 training times a day)is some version of a WOD, though not generally Crossfit as those require equipment my home or local park don't have. I either create my own or I subscribe to several companies/groups/trainers that provide free WOD for people from official Crossfit, to home based Crossfit to Special Operations specific, to Paleo fitness, to Strength yoga, obstacle racing, to functional training.

Crossfit is not a franchise, each gym location is their own business but the main company will post a worldwide WOD on their website so people all over the world can do it and post their results.