3 legs inherently stable because any 3 points in space will lie in a
plane i.e. the ends of the legs and the contact points on the floor.
Hence 3 legs will always all 3 make contact in ordinary circumstances.
4 legs may have one leg out of the plane, or one point of contact out
of the plane and hence high probability of rocking a bit. Most
furniture is a bit bendy and so will settle if left in the same place
and eventually stop rocking.
If you want a stable stool whether 3 or 4 legs then its important to
design it so that the legs are splayed a bit to extend beyond the edge
of the seat/top in plan - then it is less likely to tip if you stand on
the edge - though it will if you rock it enough.
Any old wood will do more or less.

cheers

Jacob