There's something beautiful about a tree stave you cut and cured yourself, but if you want to try your hand without a lot of initial wait (and emotional investment), it's worth taking a stab at a board bow. That way, when that sweet piece of osage or hickory is ready, you have some tillering experience under your belt already.
You can get a decent piece of hardwood at the lumber yard/HD for $10-15. They usually have red oak at a minimum, and even HD typically has black walnut and cherry. The only trick is you have to be willing to spend some time finding one with really straight grain.
As indicated above, almost any wood can make a good bow with the right design. Traditional Bowyer's Bible IV has an awesome chapter on the relative strengths and idiosyncrasies of different types of wood.