Is a pony or a horse easier for a child to learn riding on? I know mares are generally more gentle then stallions so they are better but I decided it was best to ask for some advice.

There is no magic answer. Stallions are not always hot headed, mares are not always cranky, and geldings are not always placid. So long as the animal is well trained and fits the child it will be fine to learn on. Also keep in mind there is a difference between a pony breed and a pony height. Anything 14.2 hands or smaller is a pony. This can include TBs and other horse breeds.