I've made quite a few sticks over the years, so I thought I'd throw in my two penn'orth...
A stick is a very personal thing, and the most important consideration is whether YOU like the look and feel of it. I like 'em straight and smooth, others like 'em gnarled and knobbly.
General points:
Don't get too hung up on how strong the wood is. The phrase "bear your weight" doesn't mean you will have to be able to pole-vault with it. You may well use it to help you jump a stream, so you don't want it to bend too much, but in all honesty I mainly just like the feel of a stick in my hand and it's primary job is thrashing nettles. Pretty much anything over about 3/4 of an inch in diameter will be fine.
I reckon sticks look best with the bark on, e.g. Hazel, blackthorn, birch. In this regard, I have found ash bark becomes badly wrinkled as the stick dries, and looks and feels rubbish.
The accepted wisdom, as Indoorsout says, is that sticks should be seasoned slowly without artificial heat, to avoid splitting. However, I get terribly impatient and have frequently thrown caution to the winds and stuck it on the radiator. True, it is more likely to split, but you can compensate for that by cutting them over-long. They don't usually split more than about 3-4 inches.
Trim any side-shoots/buds off while it's still green - much easier to get a good, smooth result.
Whilst you can straighten sticks with curves in them, you can't straighten kinks or doglegs caused by side-branches, so unless that's what you want, leave it on the tree.
My thoughts on particular types of wood:
Hazel - My favourite. Beautiful bark in lots of different colours. Nice and straight, found everywhere, easy to work when green, perfect combination of stiffness/flex when seasoned.
Blackthorn - Legendary strength, lovely bark with knobbly buds which turn a reddish colour when cut. Quite hard to work when seasoned. Well-protected by lethal spikes so always take secateurs and gloves when hunting blackthorn. Oh, and for some reason the stick you want always seems to be right in the middle of the densest part of the thicket!
Birch - Also has nice bark. Grows all over. Lovely to carve. Too bendy when green but seasons into a firm, sturdy stick with a good, slightly springy amount of flex. Can be difficult to find a sapling long enough which doesn't taper excessively.
Beech - Very strong when seasoned but almost impossible to find a length which doesn't zigzag due to frequent dog-legs.
Alder - Seasoned wood has a completely different character from green. Becomes surprisingly hard and strong when dry, grows like a weed, good and straight. I generally strip the bark off, which you can pretty-much do with your bare hands when green. You can hollow out the pith and carve a whistle in the handle.
Willow - I haven't had much luck with this. Unattractive bark and too bendy and insubstantial even when seasoned. I'm talking here about the species which grow in the UK. In the States they have Diamond Willow, which by all accounts makes a great stick.
Sweet Chestnut - Common in S.E. England, grows straight with only a slight taper. Bends well. It's what NHS walking sticks are made of. Most often stripped and chemically-stained. I think there are better woods out there.
Oak - Great if you can find the right piece. Extremely tough wood, so best to do your cutting and shaping when green. Main problem is that it tapers quite drastically and in steps, especially above the frequently-occurring side shoots. I am currently "training" a few saplings by snipping off any new shoots as soon as they appear, to see if I can get it to grow smoothly. So far it seems to be working.
Sycamore - Boring.
Maple - Very tough wood (butchers' blocks, dance floors) so work it green. You can find straight sticks with a bit of effort. Disappointing bark and not much better when stripped unless you stain it.
Dog Rose - Another surprisingly tough wood. Lots of perfectly sized shoots coming off a main stem, which often form perfect handles. If you leave the thorns on while it dries, then strip it, you get an attractive mottling on the shank. I often stain them by wiping with strong black coffee.
I think that's enough for now, but you can get some great ideas from
Bob's Stickmaking Pages
Hope this helps.
Demob