I think most new travelers find themselves wondering these exact questions (like myself!!). From speaking with several different recruiters, I've come to the conclusion that it's not the company so much as the recruiter. And with each assignment you take, you'll learn new things to ask/watch for with the next one. Happy searching!
Perhaps you could go PRN at your current job until you agree and settle into a contract. A friend of mine is doing this and the supervisor took it extremely well. I think her being upfront and honest, but also still willing to work and help out, made the difference. Good luck!