My guess is trees that grow extremely tall and narrow are probably good candidates - they must suffer some similar forces.

Some woods seems hard and brittle, like Oak - and some are very heavy (not to mention hard to carve!).  Seems like Eastern White Pine is always my best option at the lumber store, they sell it rough cut and it's pretty easy to get stuff thats 2" thick, 8" wide and not uncommon to find 12' boards with very few (if any) knots.

I like spruce, and fir - around here lodgepole is plentiful but we have to mill that ourselves, you can't buy the lumber.

I think tight grains are probably better - but I think to some degree we have to work with whats available.

  I'd avoid woods like maple - very strong, but heavy and the issue of weight could really become an issue when its spinning fast.  I think light weight wood has to be best so long as the grains are reasonably tight and its strong.  

Regarding how it's cut - I think anything has its pros and cons.  Vertical grain seems best, but I think it's more prone to cracking especially at the tips.  Usually when I pick wood I worry a lot less about the way the grain runs than I do knots - or pitchy/brittle areas.  I've used vertical grain, slash grain - usually its somewhere in between.