Best Jug Wine - red & white
Most jug wines are undistinguished, and one of the reason they have little character is that the mass production wineries save money by putting as little grape in as possible. Of course, there's a big market for wine with little wine character in this country, so it would be foolish for them not to provide this product.
You want to make sure you're buying real wine, first of all. There are a lot of products available in this country that stretch the definition of "wine" beyond what is reasonable. Skip wines labeled "with natural flavors". Check the alcohol content to make sure it is in the same range as bottled wine of the same style. 6% wine is not a quality product. Don't buy wine in a cardboard box unless you enjoy the challenge of getting the last liter out of a scrunched up baggie.
What kind of wine do you like? If you like the chardonnay or pink zinfandel styles, you'll probably find one you like for drinking. How much and what kinds of wine do your recipes call for? A lot of the these wines don't have much of that winey character to impart to your food. Since you say you're not much of a wine drinker, you'd need keep your jug in the refrigerator after opening it. Probably you'd be better off buying an occasional 375 mL bottle, and that way you can compare different styles. Save the jug wine for sangria at a party.
I don't know where you are writing from, but here in Washington DC, my favorite low-cost jug wine is from Italy. The brand name is Citra and it comes in both red and white. It is from the Italian region of Abruzzo (in central Italy in the mountains and on the east coast) and the various varieties--Montepulciano d'Abruzzo, Trebbiano, and Sangiovese) are all very drinkable and extremely reasonably priced. I get them on sale for $5 for a 1.5 liter bottle.
For $10 or so, you can get "jugs" of decent Italian chianti or French regional wines. Other good values are from South America--Chile and Argentina.