I'm only going off of what the top right of your post says.... which is 2004 4x4.
Clicky: Chart of maximum tire size
Assuming you've got stock sized tires now, they should be 245/75R16 or 255/70R16 on 16" rims. If you're wanting to keep your wheels, I would bump to a 265/75R16. Gives it a nice beefy stance without any adverse effects of adding larger tires.
I hear good things about Falken Wild Peak A/T and Goodyear Duratrac tires. Discount Tire lists them at $145 and $197 respectively. The Goodyears carry the snow flake emblem meaning they're a traction tire and can be considered a winter traction device. Another good option is the tried and true BFG All Terrain price at $199.
Goodyear Duratrac: Tire Details - Discount Tire
Falken Rocky Mountain: Tire Details - Discount Tire