It's based on your definition of what is either "pretty enough" or "adequately strong" depending on which characteristic is more important to you at the moment. The choice of wood for a handle is a personal preference thing, whether you are making a rustic re-enactment knife or a high-glitz art knife or anything in between.
Drying can be as simple as laying it on something so air can get at all sides of the piece and waiting for the moisture content (MC) to stabilize. If you are drying it indoors, it will usually stabilize in the 6-15% moisture range depending on where you live and time of year. Obviously, a desert summer environment will dry the wood to a lower MC than the soggy winters along the NW coast of the USA.
Since wood loses moisture faster through the end grain than the face grain, if the wood is green (freshly cut) it helps to seal the end grain with either wax or whatever paint you have laying around. Anchor Seal is a commercial product for just this purpose. Sealing the end grain helps prevent the wood cracking (called checking) due to the ends of the wood piece drying faster than the interior parts of the piece.
For stabilizing wood, let me point you at the gold standard for it:
Wood Stabilizing Specialists, International (WSSI). These are the folks that many professional knifemakers use and count on for stabilizing their knife scale handle material. You send them the wood and they stabilize it. They also sell pre-stabilized scales. WSSI enjoys a reputation for quality work and high customer service.
Any of these woods can make knife scales. But, as noted, the fruitwoods will likely have a little more character than the birch. However, I've seen some mighty impressive figured birch wood, most notably Masur birch and flame birch.
If you want to buy some wood to make your own handle material, here are a few vendors with some amazing wood available (plus other knifemaking supplies):
http://www.gilmerwood.com/ (specifically
http://www.gilmerwood.com/knife-block.htm)
http://www.alphaknifesupply.com/
http://www.knifeandgun.com (K&G)
http://www.knifemaking.com/ (Jantz Supply)
http://www.texasknife.com/store/s-pages/TKS_MainframeStore.htm
http://www.knifescales.com/
eBay always has a bunch of knife scales sets for sale as well.
... and a page with a lot of info on some of the various species of wood used on knife handles.
http://www.jayfisher.com/Custom_Knife_Handle_Materials_Woods.htm