bow wood?

[Springbuck]

I steal most of it.   I just cut a bunch of mulberry growing in a ditch beside a road.  It was outside the fence, so I assume it belongs to the city.  They have also cut it back repeatedly, so it won't grow out into the road, thus, I assume they don't care.

[mikekeswick]

Good advice above BUT the grain on any board should be next to flawless if you plan on making it unbacked. Beginners rarely choose great boards as reading grain isn't the easiest thing to do with no experience of what to look for.  The only thing holding any unbacked bow together is unbroken wood fibers running the full length of your bow. If you can't find a perfectly straight grained board find some rawhide and plan on backing it from the start.

[joachimM]

Saplings with a bendy handle are easiest and fastest IMO, unless you happen to find a very good board right away.

But wrong time of year to cut saplings as the under bark surface now only has weaker early wood. Leaving that aside saplings are my first choice for beginners.
Cut a branch 150 to 180 cm (5-6'), rough out a thickness profile (leave full width), debark the back (leaving till here protected it against accidents), seal it with a thin layer of carpenter's glue (two coats at the ends) and let it dry for a few weeks in the driest place you can find (not full sunlight).
Wheigh the stave regularly to monitor moisture losses. When it stops losing moisture you gave what you need.

Better start with a handful of staves, some may warp or split nonetheless.

Branches or saplings: as few lateral shoots as possible on the back. There are dozens (hundreds) of species you can use for this, but avoid conifers other than yew as well as the poplar family (cottonwood, willow, poplar, aspen, ...) and alder.