Rear Differential Gear exchange

Hello to all. I have just joined the club.
I have a 1998 Suburban that has play in the drivetrain. I just had the transmittion rebuilt and the mechanic said that the universal joints looked OK. I am mechanicly inclined and am planning to replace whatever parts are worn. I am assuming it is the pinion gear but I would like to hear from anyone who has had a similar problem and what is the best course of action. I have not dug into my Chiltons manual as of yet but, I'm assuming it will have good directions on removal and replacement. Thank You.

I am not sure what the pinon gear to ring gear backlash spec is,but if you are looking to reduce the backlash,I believe that by re shimming the carrier bearings to move the carrier closer to the pinion gear should take up some of the backlash.I think that a Chilton manual should explain it.If there is a specific one for drive train components,that would do it.
chuck's