Yes, build a tillering tree and get the tools you will need as your staves dry. If you get too impatient, you can buy a stave already seasoned, use a board, or try to speed-dry one of your hickory staves.
I would NOT build a tillering tree like the one in the video above... well, not exactly like that one. I wouldn't even put one of my bows on it and draw it.
You can just as easily build one that is infinitely more versatile and mimics your shooting style. Notice how his pulley is anchored/unmovable, and is located so that it pulls the string from the center of the handle... have you ever drawn a bow like that? Do you suppose you ever will? My advice is to tiller it, and precisely time it, while replicating your bow and string holds on your tree as closely as possible. It's no more difficult, and you will make better bows because of it.
I have a piece of 1/2" drill rod held in two 1/2" pillow block bearings mounted to the wall, way down by the floor, directly under the cradle of the tillering tree. The bearings are about 12" apart, and the 1/2" shaft has 4 pulleys on it. The pulleys are positioned to replicate either a split finger or three under string hold, regardless of whether the top limb is facing left or right on the tree. They are also easily relocated as needed by simply loosening a set screw in the pulley. Even though they're movable, I put four pulleys on the shaft so I don't have to move them all the time. They were cheap. I can post pictures if needed.
Get Dean Torges' book, Hunting the Osage Bow. It is geared mainly toward osage selfbows, but much of the information in it is easily applied/adapted to hickory and other woods as well. It covers tree selection, caring for/curing your wood, tool selection and care, the bow building process, finishes, etc. Best money I ever spent on bowmaking. I have the Traditional Bowyer's Bible series... they're good too.
You will need a drying box to bring your staves to the appropriate moisture content... unless you can accurately control the relative humidity where you store your wood. I have a dehumidifier in my shop.
Forgo the cheap dept store rasps that chew and tear wood. Get a good rasp. A Nicholson #49 is a beautiful thing. It's an investment you'll fall in love with. A farrier's rasp is very useful too. Buy new ones, not used/dull ones.
Cabinet scrapers, straight and gooseneck. Learn to sharpen them correctly.
All such stuff and more is covered in Dean's book.
He also has some EXCELLENT articles on his website... stuff that wasn't covered in as much detail as it was in the book. But still... get the book
Here's the link to Dean's article page...
http://www.bowyersedge.com/articles.html