Think of it more along the ways of a fanatic. Every fanatic starts out somewhere before becoming one. The Rockets believe in the goals Giovanni has and the force of their organization. They believe themselves to be superior to all others that are not higher ups. That's how most fanatic groups work and how Team Rocket seems to work too. Read the dialogue in the games and they give off that impression.
The character had a life prior to joining up or wanting to. The benefits could be great or they could be short-lived depending on your actions in any organization. As a member of Team Rocket, if you get caught, you may or may not be bailed/broken out or rescued. Depends on if you should be able to escape yourself, why you are in jail or in holding, and how you were caught/found. But if you have good senses, the know-how and a bit of luck, you'll do just fine. The pay of a cop compared to what a member of Rocket makes is probably much less. Risky jobs pay more money; higher the risk of a job/mission, the better the reward.
You have a loved one in need of a hospital to treat their illness, and you have the chance to make you both set for life? Not forced to join it when it's pretty much freely handed to you. Joining an organization in this kind of circumstance leaves you with the chance you will be used or sometime your loved one, if known, will be used as leverage. You could also just join the police, earning your wages legally and doing a service to the community of your area. Believing in justice over a known crime organization is up to a sole person to decide. The pay either way is great, plus the benefits help with medical bills. No other jobs happen to be available at the time - Leaving the police and Team Rocket as your options.