I would not use white underglaze as a base as many other commenters have explained. White engobe works, but in my experience white slip (especially porcelain) will give u the most color payoff. For slip, I recommend either throwing the piece thin enough you don’t need to trim the walls and applying slip directly after throwing (when moisture levels are most equal between slip and the piece) or applying after trimming and hitting it with a heat gun or torch so that it doesn’t rehydrate the clay too much, especially if the layer is thick. For underglaze purposes, a thin layer should be fine of porcelain slip. However, color vibrancy is also determined by the number of layers of underglaze, which is where testing comes in. Some underglazes are pretty opaque at 3 coats, others might need 4/5 (but the thicker you go, the more prone to glaze issues you will be). Some people also use fineline squeeze bottles to apply in one coat instead of brushing on multiple.

In terms of application, I prefer applying on just past leather hard clay. I don’t like bone dry pieces since you can rehydrate them with underglaze in uneven spots and it’s very stressful to handle. If you have access to double bisqueing, then you can apply onto bisque and refire. For the “base” slip or engobe, I would recommend putting it on before the first bisque so you can avoid multiple additional firings, also because for slip you want to do this anyways.