The best bow wood is the wood you have available.
That is a bit tongue in cheek, but use what is available to you right now. For me, local woods are elm, hickory, ash, hophornbeam, birch, and some others. Elm is amazing wood, if a bit challenging to harvest due to interlocking grain. Osage doesn’t grow in the New England area, so that is not a wood I worry about. Same with yew – I do have some, and it does grow in Massachusetts, but is very rare in my area. Lemonwood in the US is nearly impossible to acquire due to the Cuban embargo, but if you are lucky, you can find it in board form, as I did a few years ago. A hardwood specialty dealer can be a godsend to get started sooner, and if you can visit yourself to select the right boards for your needs, all the better.
Putting off making bows until tomorrow sometimes mean tomorrow never comes. Just jump in and have fun. And, there are a number of Stone Age bows you can replicate (and that are nearly or completely intact and documented) not just Holmies and Mollies. A great book on some of these designs is “The Bow Builder’s Book.” I got my copy for 24 bucks on Amazon, and it is strongly slanted toward Mesolithic, Neolithic, and some other periods. Internet research can help you find other bow styles to replicate or get inspired by. The 4th volume of the Bowyer’s Bible has a pretty all-inclusive listing of ancient bows by Tom Mills that can help you do the research.
Dane