And don't assume that ALL primitive arrows were made just from shoots! The Cherokee and many others made split hardwood shafts from hickory and cedar. These woods naturally grew very straight and were fairly easy to split. By carefully choosing your boards from the lumberyard, you can split then down to 1/2 inch squares and with a small hand plane you can turn the 4 sided shaft into an 8 sided shaft and then to a 16 sided shaft and then all you need to do is sand them round! Or a little cheating and ordering premade shafts from any number of reputable dealers won't break too many of our hearts!
If your goal is to do the whole shebang from scratch the very first time out of the gate you are in for a lot of hard work and probably more than a few disappointments. Starting with making your arrows first or making your bow first and using storebought for the rest is quite ok, too. Whatever you chose to do, we can all pitch in with helpful pointers, tips, and experience. There's LOTS of that around here to spare!
