Just saying that your first one will likely not be great, or even good. Doing it properly is different than doing it perfectly. This is a process not a product. You will make mistakes and your bows will get better over time. There is no instant gratification here.
I have made bows from ash, elm and oak from the list in the link. Most were stave bows but I have made board bows from oak that were passable. In my experience, good ash is the best. Elm is second. Oak is last. The quality of the individual piece is most important though as they all have great variability in density and quality.
All that said, I prefer to cut my own so that is what I would do.
Personally, I would not spend my time and money making a composite bow from any of them. But I have lots of good bow wood from all the years and effort I have put into harvesting it myself.
If you are going to make good bows, you need good bow wood. You can find, cut, and process it yourself or buy it from someone who has done it for you.