It's really tough to choose simply based on the wood's name. Variability among the ash and maple is huge. So, the individual piece would decide for me. The grain is the first determinant. If you can find boards with equal grain, the heavier of the two will be the better bow wood, all things equal. Make your first bow overbuilt like in Ferret's Board Bow Instructions and you should be fine with either maple or ash. I don't know about cherry.
I wouldn't back a first board bow made from ash or maple with sinew. It's too much work and adds a pretty high degree of complexity. Put linen or rawhide on it instead. Best of all is no backing, assuming a good board choice.
Design determines the best choice for a backing. Quality of wood determines the best design. Long, overbuilt board bows are not a good candidate for sinew. At best, you will get protection from lifting a splinter and sinew is heavy so it will slow wide, long limbs down.
Bamboo is graduate work in my opinion. Learn to remove wood accurately first. Then tackle the tougher stuff.
Ferret\\'s Board Bow Instructions