I'm new to boating, but I am experienced in dog-ging (I own five, I amateur race/lure course/show them, blah, blah, dog owner credentials blah).
I now can't remember if the OP ever owned a dog, but assuming this is new...
I wouldn't wed to one breed, or mutt, or mix-a-poodle; the important thing is to find that young dog with a personality and temperament that works for your family and then a size for your boat. If you do love a certain breed, try a breed rescue -- almost all breeds have them and have dogs who need homes. They tend to be well-vetted, and the foster homes have a pretty good idea of what you are getting, personality wise.
I find myself thinking of a post I read recently about being out for a long time on his boat, and then grousing that his nine month old lab peed on his blanket. So that said:
Whatever dog ends up speaking to you, don't get a young puppy and expect it to not pee, poop or barf where you don't want it to. It may well chew or do other annoying but very normal puppy things to your boat, your blankets, your food, your shoes, your fingers, your hat, your expensive handheld GPS left on the seat... You get the idea.
A general rule of thumb is however many months old your puppy is is about how often it'll need to go. Nobody should be selling young puppies, but for example, a six month old puppy will need to relieve itself roughly ever six hours maximum. An excited or anxious puppy might do it more often.
I'd also caution that a dog might feel a bit overwhelmed with the excitement and newness of being The! New! Dog! and a boat dog all at once. Take it slow and make sure the experience is positive for him/her. It'll look to its people for cues on how to react to situations.
My five or six doggie cents. Good luck in your search!
(and since we are showing off dogs, here's one of mine. Not really a boat dog.)