You have it backwards though, boots should be your first priority, then bindings, then board.
Check the boot fitting guide for more info.
As for bindings, it's personal preference. I have Rome 390s (as well as a few others here). A lot of people also like the Burton Cartels. It also depends on what kind of riding you do.
As for the board, 155 may be too short for someone as tall as you. I am 5'10" and I ride a 156. You may be better off with something like a 160. I don't really know the difference between both boards, but I do know that Never Summer makes some of the best boards out there.