Don't think that the wood matters, as long as you look for something that has a nice wide 'Y' shape where both sides of the fork are at about the same angle from the main stem, and about the thickness of your thumb or middle finger.
I would be more concerned about the shape, than the type of would, as long as you do not pick something hollow like
elder. You should be able to test its strength, by just gripping the ends of the fork and pulling or pushing them. If you grip the handle with your thumb and first finger well up the sides of the fork, the way my Grandfather taught me, you will be supporting the wood anyway, but remember to move the hand that you are holding the catapult with down sharply as you let go of the part holding the missile, otherwise you may well hit the back of your hand. You do not require long ends on the fork,just about the same length as the handle. I used to be able to hit a target the size of a 50 p from across a country road, but I have not used one for years , though I still have one. If you take "Y" as a pattern you will not go wrong.
Only certain woods tend to fork into equally sized branches, most have a thick leg and a thin one, but I forget what
wood I used. If I remember I think wood from a Broom bush is fairly strong for its thickness. I would also suggest that
you use 1/4 square or round elastic sold in Gun shops, sold for the purpose, rather than the hollow stuff you get on modern bought catapults. Split the ends of the fork and wedge the rubber in then bind the wood shut at the ends to hold
the rubber tight. Best of luck and good shooting.
