I'm sure someone will correct me if I'm wrong but when you say stay on their own, I don't believe its possible to practice real estate sales and call yourself a "realtor" when you first start. You need to be a sponsoring broker to do that and I think the time requirement is 2 years working with a sponsoring broker before someone can apply to be a sponsoring broker and be "on their own". You and I are on similar paths. I'll be taking the exam within 2 weeks and my plan is to work with a larger RE group (Re-max, Berkshire, Century 21 etc.). I'm choosing to do so because even though they will take a larger % of my commission, I've heard that not all realtor groups are created equally. What I mean by that is it's important, as a new agent, you have access to the resources you're going to need to do your job well. While some of the smaller groups might offer a 80/20% for the houses you sell, they might not offer the same quality of resources that other places who take a little more out. That extra % that they take out will go to having a clean office, maybe a personal assistant for the brokers, office supplies, etc.
Im sure others can elaborate even more. Good luck on your journey!