The tighter and more closed the grain the better. Hard maple is the classic choice followed by others like cherry and walnut.
I would avoid any woods with very open grain such as oaks, ash, locust, sassafras, etc. Open grain is simply easy access for micro critters.
There is nothing wrong with using softwoods for cutting boards as long as they are for light use. An example, my parents have a board about 8x8 which was simply a cutoff from a pine board. It was heavily oiled and has been in light use for 30+ years. If you start using a meat cleaver on it or heavy cutting at every meal then it won't last long.
I believe that while oak is an open grain wood, it is still fine for boards. I have used it for many myself, using both red & white oak. There was a study by a CA college where they determined that even if bacteria gets into the open grain, then natural abilities of the wood would kill the bacteria anyway.
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