European Oak, Ash, Hazel, Maple, Elm work well, birch moderately well (make it wider). I would make (and do so regularly) a bow out of any of these, flatbows are easiest but ELBs are possible with careful tillering and perfect wood, Elm and Hazel are better ELB woods. Often oak is easiest to get, given a choice i would go with maple, but teh differences btw. species are less than difference btw. individual trees.
Yew tends to be expensive or protected, Exotics, hickori and osage can be imported, as can bamboo.
German Dicks GmbH sells boo and various woods, as well as tools, but expensive.
K