I no longer drink, but I used to, exponentially. It was quite a hobby of mine that I became very good at. The only boxed wines I know that are under $10 are the liter sizes.
My suggestions: Three Thieves Bandit Pinot Grigio or Chateau de Bonhoste Bordeaux Blanc. Three Thieves (if I remember correctly) is 9 dollars. The Chateau was either $10 or $12, but I remember being able to purchase to 3 liter boxes for less than $25 at Total Wine and Spirits.