from personal experience from many years of owning 4x4 for off roading mud bogging, dirt sand and snow bf goodrich has the toughest tire with the best traction out there. I watched a 4x4 off road series where a group of guys got together with the publisher of well known magazine, and spent several weeks on a trip where they would drive their rigs several hundred miles and then go find some rock crawling mud dogging cliff hopping absolutely awesome serious off road terrain. All of them took bf goodrich and explained why. It was the one tire that was tough enough to do it all, and had superb traction when they needed it the most trying to crawl up several foot ledges, At one point this guy with a ford 3/4 ton long bed with a built 460 was trying to get up about a 4 foot ledge. as he opened up the secondaries on the carb, the spotters all took off in different directions, and as the tire smoke and dust and dirt completely obscured the truck, you could hear that 460 winding up.Then it stopped, as the smoke cleared the truck had made it up the ledge, but was laying on the drivers side (least wise he made it up)
I have used bf goodrich all terrain tires on my rigs, mainly because it works well in about everything. but if you want an aggressive mud tire, bf goodrich has that covered, its called a mud terrain and price wise is competitive and cheaper than some of the overpriced less durable stuff out there.one reason these tires do so well is it has about a two inch thick rubber layer under the tread. which makes it very hard to stick or rip something through it. I went up to a well known 4x4 trail here in the north part of oregon, and 8 out of ten trucks all had the bf goodrich all terrain (the trails were covered in sharp rocks)
Americas discount tire has a web site that besides being within a buck or two of costco, you can see a customer review section where the customers all write down their comments good or bad about what tire the bought. If you get over sized tires, getting them to balance properly is about the only hard thing you have to figure out, you may have to go get the tires balanced a few times until you get it right. walmart can special order tires, and will meet or beat costco or americas tire,( I don't know if walmart will order and install oversize tires though) and an online website that I have heard of but not used yet is tirerack.com, and I hear they have a section for tires they tested and rated, but I have not seen it. best of luck, there are manufacturers rebates off and on so be patient and do the research first.