Willow and a few others are customary, but following conventions like this isn't a must in magic. Pick wood from a tree that resonates with your personal energy by meditating under it.
Interestingly enough, the Wiccan rede talks a bit about wood correspondences. I'm not saying you must follow it, but of interesting note.
Nine woods in the Cauldron go,
Burn them quick and burn them slow;
Grape and fir and apple tree,
And Hawthorn are sacred to Thee,
Willow, hazel, rowan, birch,
And oak will guide your every search;
Elder be the Lady's tree -
Burn it not or cursed ye'll be.
Birchwood in the fire goes
To tell us true what Goddess knows.
Oak trees tower great with might,
Burn the Oak for God's insight.
Rowan is a tree of power
Causing life and magick to flower.
Willows at the waters stand
To help us to the Summerland.
Hawthorn burn to purify
And draw the faerie to your eye.
Hazel tree, the wisdom sage,
Lends strength that comes with honoured age.
White the flowers of Apple tree,
The holy gift of fecundity.
Grape grows upon the fruitful vine,
Sacred gifts of joy and wine.
Fir's ever greenness declares life
Succeeds beyond any strife.