What is your primary carrier? US carriers are much more lenient than European carriers, which are often strict about weight too.

I would think 14x22x9 would the biggest that would not have to be turned sideways in most newer style overhead bins. The problem is that a lot of luggage makers say their bags are that size but are often larger since they don't count unmovable handles, feet and wheels that stick out. Those cause the problems with the doors closing.