Money moves to make before leaving your job for another

Dear Dr Pesa,

I am a 25-year-old working at a big firm, but I’m unhappy with my pay check and work environment. I applied for several jobs and managed to get two good offers... salary-wise; the rest of the packages are not good. For instance, they both don't offer health insurance, no pension, they are contracts - I'm currently a permanent and pensionable employee, among other issues. But the pay would be really good. I’m a little worried about joining a new company, diving into the unknown. Whichever I choose, I don’t plan on staying there very long. How can I better prepare for my next move?