BONUS - no trees to cut problem
Maybe someone thinks "Archer, all this sounds good but I still don't have access to any of the tree species you listed!". I would say to them to not despair, as solution is easy and very cheap.
This is a short post, but a bit overdue, I keep forgetting to write it.
So if you don't have access to property where you could cut tree or you don't know someone who could give you one, you can attempt to make "board bow". This is an ultimate beginner bowyer project and many bowyers started with a board (including me).
One should go to these stores where they sell processed lumbers and look for ash, red oak, maple or hickory boards (for american bowyers). Boards are cut from trunks in couple of ways:
1. Plank selection
Boards already come dried and seasoned so you can start to make bow as soon as you get home from the shop.
You should look for the board that has its grain as parallel as it can. Look for example at the quarter sawn and rift sawn boards. They are a pretty good choice. Also, the tighter the grain, the better.
What this means is that you would come to shop and carefully sort out plank on the side and at the end select best from these you sorted out. At the end, you may come home with just 2 boards. Sometimes more. Really depends. Don't rush yourself with buying if you are not satisfied with grain.
2. Proceeding further
Go to the point in datasheet where I put the drawing of bow layout. Select side with best looking grain to be back of the bow. Trace the layout on the board and follow the rest of the datasheet.
Conclusion
This is a much easier thing to do for a first timer and maybe I even recommend doing that instead of starting with a tree. But it depends on you. Maybe you want to get your hands on the harder process as you like challenge and that is fine.
In any case you will get a fine shooter. It may look a bit "perfect" at the end, opposed to the one from the tree which has knots and imperfections. Some people despise board bows and at some time they were greatly underestimated for no reason. People started to appreciate the more when big faces among the bowyers started doing them.
Here are some examples I saw on internet: