How often are you accepted to your first choice assignment?

Two years is certainly better and you will indeed be a more accomplished clinician. This will give you a better choice of assignments and less stress at the end of an assignment. You are basically a free agent as a traveler, and the more you bring to the table, the more in demand you will be. That includes travel experience so don't be too picky on your first assignment. You need a successful travel assignment on your work history.

Once you are a traveler, it will be easier to keep going. There will always be some stress getting the next assignment, and then starting it. Often I've delayed looking for the next, but it is usually easy to extend a few weeks. You are a known quantity and more valuable than the unknown new traveler who must also burn money to be oriented.

two years is ideal. the more skill and experience you have the more bankable you are

I am currently on my first travel assignment. I was lucky and was offered a contract at the hospital that was my first choice. At the time of interview I had already applied for and received my license for that state. I am traveling with 5 years experience as a nurse and over 12 years in healthcare. I have been warned that you should not turn down an assignment that is offered, because the hospital may not accept you in the future. With this in mind, I only had my recruiter submit my application to hospitals that I was really interested in working at. This may mean you have to wait a little longer for an offer, but if you have planned and prepared for this you should be okay.

Congrats on your first choice assignment! But you know, with between 300 and 400 travel nurse companies, and (depending on how you are counting) between 2,000 and 6,600 acute care facilities, you can afford to burn a few bridges. While I certainly don't advocate being submitted to a hospital you will never accept, sometimes you discover during the interview that you not a good fit for the unit that wants you. It is perfectly OK to turn down such a misfit as that is good for everyone. Everyone understands that or should, and if they want to blacklist you for all time, well did you really ever want to work with such management anyway?

It certainly is a personal choice to be picky or not, or have no down time. Different strokes! I will say that I have never had an assignment in 20 years that was not good in some way, so if you are too picky, you may miss out.