LT and LTZ are trim levels. LT is a step above the WT (work truck) and has more cushy things that come with the package and more options available like leather, sunroof, etc. There is usually a 1LT and a 2LT option package. LTZ is a higher tier for Chevys. It includes everything in the 2LT package and then some. Often with the 2LT and LTZ packages there are ride enhancements. For example in the case of my HHR, its a 2LT which has FE2 sport suspension, not available on the LS or 1LT. In the case of a truck I don't know.
Z71 is an RPO code for the 4WD package. Depending on the year that includes 4WD, the G80 locking rear end, and a skid plate covering the transfer case.
4WD could affect handling but in a full size truck it won't make that much difference really. My '08 Sierra has the Z71 package and rides pretty nice. Keep in mind, they are still trucks. Although the 2014s and 2015 ride better than the previous generation.
The sales brochure has everything you need to know about these packages.