1. Avoid a Tinted Primer
Many spray primers come in either white or light gray. Light gray primer seems like it wouldn’t be much of a problem, but the slight tint does show through a little under the first coat. If you plan only to paint 1 coat of paint, the tinted primer will basically force you to paint a 2nd coat in order to fully compensate for the tinted primer.
Even with two coats, I would still use a white primer, just to avoid the possibility of not getting full coverage on the 2nd coat of paint and having the tinted primer show through.
2. Time Saver
If you are painting your piece white, there is a major time saver you can take advantage of if you plan to paint with a brush. Once the piece is primed, I would apply the first coat of paint with a generic white spray paint (as closely matched to your 2nd coat as possible).
The odds are good that the first coat will never show through unless the piece is dinged and even at that, any minor shade difference in your 1st and 2nd coat of white, would be unnoticeable. Then, apply your chosen 2nd coat. This will more than cut the time you spend on your first coat by a half – at least!