I have nearly always used material from a birch tree. I have found that other trees are either no good at all (e.g. oak), or are more suitable for something like a cane (ash, rowan). Willow is quite similar to a birch, though you can't make a particularly severe instrument out of it, but it tends to break more easily than birch twigs. I have never been able to understand why they used hazel (for a few years) in the IOM; I have never found it satisfactory at all, and birch branches, if properly chosen, can punish as severely as any kind.
The best advice I can give for making a birch is "trial and error". There isn't really a substitute. However, here are a few points to bear in mind.
(1)If possible, gather your twigs when there are no leaves on the tree, and store them in water (preferably with a lot of salt in it). Removing zillions of leaves is a real chore, and the green tips of summer branches are soft and don't sting well. Twigs in water will kep for several months, though eventually they become too weak to be much use (they then break too easily in use).
(2)You can easily gather the sorts of very-branched twigs needed to make a spray sort of birch almost anywhere you can find birch trees. For straight rods, suitable for severe punishment, it is best to find an area of land that is being re-colonised by young(ish) trees. Young trees in this sort of situation produce a lot more of the straight branches. If places where there are only very old birch trees present, you may find it dificult to obtain any straight rods.
(3)To begin with, try making a spray type birch about 30 inches long. This is easy to control, and not excessively punitive. It will give you the general idea. Try it out on your calf (right calf - bare of course - if you are right handed) to see if it is anything like useable. Spray birches can be made up to about 48 inches long if they are going to be wielded by someone strong, but you may find that about 42 inches is a more practical upper limit. Very small and light spray birches, as small as 15 inches, can be surprisingly painful when applied to sensitive areas, such as the front of the thighs. Experiment to understand the difference between a birch with most of the twigs parallel and one with some side branches sticking out sideways. The side twigs in the latter will tend to punish well outside the area that you "aim at". Punishment with a spray type birch tends to be very painful, and will cut the skin if the birch is applied hard, but the damage is superficial.
(4)A birch with a small number (3 - 6) of rods that have been entirely stipped of side twigs is, if well made, a much more formidable instrument. Again, the ideal length is from 36 to 48 inches. Be careful with birches like these, and only apply them to the bottom, never the thighs. They can cut quite badly and in strong hands they can inflict really severe punishment. Note that you will need to restrain the person being punished if you use one of these birches hard.
(5)For both types of birch, adjust the twigs so that they seem "right", and then bind the handle with string. (You can do fancy bindings, e.g. with ribbon if you want.) Bind tightly at 3 or 4 points in the lower half of the birch. Again, trial and error are needed to do this right. If the handle is too rough to hold easily, which is occasionally the case, then put a layer of plastic tape over it.
Hope this helps.