i agree with pretty much everything everyone saidcept on a couple things but that is due to my preferrences.

1)31's will fit with slight to little lift,and the will fit your rims if the rims are 7 inches wide,they will have the size stamped on the back of the rim it will look like this 15x7jj or along those lines

2)both of those are good brands

3) this is where my preference kicks in i also would prefer goodyears and bfg's goodyears because they never did me wrong and bfg's because i seen them carry many trucks through some rough places.I really dont like firestone/bridgestone(same company )something about the tire compound just aint right for me and i dont like how firestone prices their stuff tires and parts they sell.here is what i would recommend if you do go bigger tires
a)bf goodrich general off roading at ko's heavy mud mud terrain km
b)micky thompson baja claw directional tread wide deep lugs great for sand and mud
c)pro comp mud terrain or x terrain x terrain moreso due to directional tread
d) goodyear the mtr is at home everywhere hand is punture resistant.
ground hawgs and buckshot mudders are also dang good,seen a ton of them back home in stuff that would make a hummer bow in shame.

4) as Sunder stated articulation,more axel travel without bumping so you can take on bigger obstacles.
5)as someone said if you have the tools do it yourself.

another thing i might add before you decide on lift and tires get a winch,they are worth it there are posts in here on different winches and their capabilities as well as downfalls