It is definitely less risk and much easier to start in someone else's gym, especially when there is opportunity for expansion. You can make use of their marketing and location to increase your student count and build you own clientèle. Make sure to have them track the martial arts gear that is sold in the pro-shop so you get a piece of that action as well, and also ensure you have all of the contact information for all of your students in case things change with the fitness club and you need to (or want to) move out on your own. Also, remember to nail down a solid curriculum and systemize everything that you do so you're prepared to bring on new instructors who will do everything the way you do it when you expand. Many of the most successful martial arts schools started in fitness clubs and rec centers before beginning their own clubs, so if you can make it happen, get your feet wet that way rather than spending your life savings on opening your own school! Good luck!