I make cards for OWH and my Church's Relief Society.
The white cardstock I use when it's the card base is CTMH's White Daisy. It's really sturdy and holds up well to coloring. The Relief Society has me do CAS cards for them.
But when I do colored cardstock for my card base I use whatever white cardstock I have handy.
My recommendation is if you think the white cardstock you're using isn't what you'd consider quality for the card base you could always use it for inside the card. Or even for stamping your sentiments on.
Good luck in finding a white cardstock that's right for you.