Too eager?

When I got my interview call last year (my first), I was so grateful for the opportunity that I snapped up the first position offered without any questions.
I'm wondering if anyone can tell me what might happen if I am offered something other than my first choice and I was to turn it down. Would that exclude me from any further consideration, or would it just put my application back on the pile for another manager or supervisor to look at?
FWIW, I'm a cook.
Any insight appreciated!

Well, it's a new year and a new application. Just apply for something different as your three choices and put cook under something you wouldn't want to do. There should also be a check mark that you can check for "I wish to be considered for the same job..." or something like that.