I think your question(s) should read;
"When you want to do travel nursing, can you design your own contract?"
"When you know what you want out of travel nursing, can you design your own contract?"
Yes and yes, and you should.
You are a nurse, with a lot of experience.
The agencies want you to work at the lowest possible rate because they get more money.
The opposite of this is always true: The reason that you should get the best contract possible is because you get more money.
It is a matter of fair and equal negotiations, it's not a matter of "until I get a few assignments under my belt". The line of "you are new to travel nursing, you have to take what you can get" is BS. Also, you should never be led to believe that your contract must be different because you are new to travel nursing.
For me, I knew what I needed; I needed the opportunity for OT, small hospital, and I needed a company and recruiter that I could like. I could have asked for more, now I know.
There are a lot of reasons an agency can't give you everything you ask for, but being new to travel nursing is not one of them.