Generally speaking, rift and quartered come in the same unit. If you want only quartered, the bundles are opened and the materials separated. This costs more. In terms of stability, rift is no different than quartered. The main difference is in the grain. Rift has a vertical grain (runs straight as an arrow) and quartered is AKA "tiger oak" because it shows a radial fleck.

Since you are going the extra mile and cost in choosing a rift cut or quarter sawn oak floor, I see your having only two choices. 1. Not to dilute the effort and effect by randomly mixing the two 2. Choose a floor pattern that takes advantage of the differences. I did library walls with rift cut and quarter sawn wood with a particular design effect in mind relying on the layout and stain to emphasize the different grains.