So, let's take a look at all the wonderful and wondrous items we can make with wood and which woods might make the best version of a magical item.
First stop, WANDS:
Yeah, kinda cliche to list wands first, but they are a foundation piece in D&D. Intricately carved or naturally grown, straight and true or gnarled and wicked, wands come in all shapes, but generally not all sizes. What is one to do when wanting to craft that particular wand? Since wands can hold charges of just about any low level spell, the options really are too many to list here. But a few examples would be:
Lightning - you will want a wand crafted from a tree that has been hit by lightning and survived.
Fireball - you will want a wand crafted from a tree that has some fire resistance or that burned in a forest fire.
Magic Missile - as the spell manifestation is unique to each caster, the decision here is up to you.
Healing - you will want a wand crafted from a tree known to have healing properties (such as birch or willow for the salicylic acid they contain).
Next up, Staffs and Hafts:
Here, you will likely want a wood that is solid and strong, something with an appealing grain and texture. Waxwood has gained popularity in use as a staff, but traditionally we look to the ash, hickory and oak trees as sources. I can see this being a good opportunity to get in some role-playing or to flesh out your characters area contacts - perhaps they know a Treant who would assist in finding a suitable log or Druid that knows of a recently felled tree. Conversely, the PC could make an enemy out of said individuals by taking a tree without permission. If one is using the legacy concept of magic item evolution (my grandfather's axe), then by all means, make sure to use the same kind of wood that was previously used.
BOWS and ARROWS:
This has always been a bit of a tricky subject to me, some games attribute magical properties to the bow, some games attribute it to the arrows and some games to both (making for a very power combination). I tend to lean to the side saying the bow is magical and imparts that magic onto the projectile unless the arrow is a specific item (arrow of dragon/giant/etc slaying). Yew and Elm seem to be popular choices, but any hardwood should be considered.
Most tanks are going to want a shield and wooden shields are historically very common. Some games create wooden armor and this is historically accurate in certain areas of the world and certain time periods. Oak seems to be the wood of choice, then covered in hides and capped with metal. The sizes and shapes obviously depend on the source.
I can see a big, ancient oak that has been hit by lightning several times and survived a couple of forest fires providing material for a lot of shields, staffs, hafts, wands, arrows and bows. When it doubt, talk to an elf or druid, those Treants are hard to find unless you've pissed them off!