As Painthorsemares said, a foal form your registered Paint mare would need a registered Quarter Horse, registered Thoroughbred, or registered Paint sire to be eligible for the Paint horse registry.
Pinto does not automatically register anything with color anymore-- mares and geldings can be hardshipped in if they meet specific color and other criteria, but intact males have to come from registered parents. Since your mare is registered Pinto, any of the pairings mentioned above would result in a foal eligible for Pinto registration as well. Pinto also allows crosses to other breeds besides paint, QH, and TB.
I don't know anything about the 1/2 QH registry. If it is like the 1/2 Arab registry, which always requires one parent to be purebred Arab, then only breeding to a registered QH would get you a 1/2 QH foal. But I am not sure if the 1/2 QH registry works like that-- perhaps they allow registration of the offspring of two registered 1/2 QHs to be registered 1/2 QH.
The Paint and Pinto registries are large active registries. They are the registries I would focus on. I don't think the1/2 QH registry offers much in the way of shows, activities, or benefits--could be wrong, but I have never heard of 1/2 QH programs nor even actually seen a set of their papers.
I would also test your mare for Lethal White Overo (LWO) before breeding. Many Paints and Pintos marked like your mare have this gene. It is not harmful when there is only one gene present but when you breed horses together that each have one gene, you run the risk of a foal with two LWO genes (it can inherit one from each parent), and that is a 100% lethal condition. If your mare is LWO positive, you could avoid the chance of a LWO affected (lethal) foal by choosing only LWO negative stallions to breed her to.