I've run a lot of different tires over the years. Here's my 2 cents.
Round is good, balanceable is good.
Most any of the cheaper carcass' made by Cooper and the Chinese no-name tires have tissue paper thin sidewalls right where they meet the tread. Pep-Boys has tires like this for their house brand. They are literally 1 ply of nothing right at the corner of the tread. The lower end Cooper carcass tires also tend to dry rot right next to the bead and crack. Mastercrafts are famous for this, often bulging out right above the bead if they are neglected in the sun for too long.
I know they are spendy, but Toyo's are very good, and Nitto's are just as good, sometimes better. I've seen Nitto's take some pretty horrendous use and hold up pretty good. I've run Hankook A/T's and M/T's I can recommend either one. Have the M/T's siped if you buy them. They are softer and the tread isn't as deep as a BFG, but they are still pretty good tires, especially for the price.
BFG A/T's are crap unless you need a good sand tire. They have a round carcass on the tread and wear the center out no matter what, unless you run them dangerously under inflated all the time. The M/T's are good, but no better than a lot of the other upper end tires on the market. Goodyears are good, some people like the Duratracs, some like the Kevlars, I ran a set of the square block pattern all terrains for awhile and they were surprisingly good at a lot of things.
Kanati has some good M/T tires, but they are super soft and my dad only got 25K out of a set, and he drives very, very conservatively and doesn't tow anything heavy, ever.
Michelin is a good tire, but I don't know if they are worth the extra $$.
If you are looking for MPG, then watch the weight of the tire. I lost 1 mpg going from a craptastic set of no-name chinese tissue paper tires to a set of Hankook A/T's on the wife's 4runner, but the peace of mind was worth it.