I dont like recommending board bows to beginners as wood selection is so critical with them. It really sucks having a bow blow on you because you chose a bad board. Although it has its advantages, in that you can start bow making immediately without waiting for wood to dry. Your call on that.
Splitting large diam trees and working them down is time consuming with hand tools. The bowmaking process really begins when tillering begins. To get large diameter staves down to tillering stages takes a while with a hatchet. Then to go head-on tillering a bow for the first time after spending time reducing it down to bow dimensions and having it blow on you is very upsetting.That's why i like to recommend saplings to beginners as they are fast to make,as functional as a stave bow, easier to learn on, and can be quick dried much more easily.
Go cut some hardwood saplings- hickory, hornbeam, elm, oak, some maples, etc at least 60 inches in length.
Rough it out so its bending a bit at floor tiller, then strap it down to a 2x4 so it doesnt warp. Let it dry for a month, then begin tillering. If it feels spongy while tillering or begins to take set, let it dry for 2 more weeks. I would go further into my method of reducing green wood saplings to bows even faster, but would take too much typing and reading.
Tools can be as limited as you want. You can make a bow with just a knife, or just a hatchet. That's how a lot of us got started.
But i recommend, a hatchet for roughing out, a knife(used at 90 degree angles to the wood) of cabinet scraper for scraping, and a rasp for more aggressive wood removal before using the cabinet scraper or knife.Some use files to cut in the string grooves. I just use a knife to cut my nocks in. Then of course sandpaper and finishes for finishing.