For the wood, I think Yew is used a lot as it is naturally a flexible softwood, And can easily resist tension. For the string on the bow I don't think grass would be strong enough or hard enough to properly pull an arrow back. That's why usually animal hair is used as the string as its more durable and strong. Plus the grass will die and wither while the hair is in fact already dead and wont deteriorate as fast.
I have never done proper bow ,but from what I have reed indeed yew tree is your best choice,your second best choice is osage orange tree.The wood for the bow needs to be strong but in same time flexible ,so it will not simply break if you pull the string too abruptly and much further.Lightweight is another very desirable characteristic of decent bow ,since nobody likes to drag around something super heavy.
Yew trees are weird ,they live very long time and even if the tree looks kinda dead from its core another young shoot appears.You need to use the young wood not the old one.
You can use another type of woods such red oak ,apple ,ash ,ceder ,but those tend to break if you pull the string too much and too hard.
I would use birch tree for the arrows and sinew (animal leg tendon)for the string.Sinew need to be dried.
Overall making a bow is an art and it takes a lot of knowledge and skills to make all to work perfect and to be balanced bow.
I am sure I have seen tutorials of bow making in YouTube,which you can check.