Hi - so you want to overland an Avalanche? It is an extremely capable truck, more capable than people give it credit for, and by far the most functional body design for solving overloading issues - secured storage, large storage area, thru cab access, etc. But as others have mentioned, it's soccer mom suburban underneath so there are weak points that MUST be addressed. The challenge of an Avalanche is that there is very limited - read that as almost zero - aftermarket parts support for items like bumpers, racks, winch mounts, etc.
Having said that - there are substantial differences between the 1500 and 2500 Avs. First, the rear diff is 10bolt vs 14bolt - meaning not as strong. Front diff is 7.25" vs 9.25" - again not as strong - and in a 2500 you CAN put a locker in that front diff if you want - can't in the 1500. Transmission - 4L60E (problematic) vs 4L80E (bulletproof), capacity (1500# vs 2200#), engine 5.3L v 8.0L, hubs 6 lug vs 8 lug.
Now - the downside of a 2500 will be substantially reduced fuel MPG. Having said that, I chose the 1500 Avalanche and spent 8 years figuring how to deal with the weak points (see my build thread that Rayra referenced) and make it essentially capable of going toe to toe with any overlanding or offroad rig out out there - with the exception of the rock crawlers.
Keep in mind - I am an overland and offload explorer - meaning my rig is my lifeline. If there are two ways to the same point of interest - I'll opt for the one that's least likely to invoke damage to my vehicle.
Now for the news - I totally destroyed my black Avalanche (Te Anau III) in an accident in October. I purchased another 02 Avalanche - except white and a Z71 rather than an NFE, and am in the process of cutting apart my old one and transferring everything to the new one.
My recommendations to you starting from scratch with a 1500 2002, I would purchase at a minimum a Z71 preferably an NFE, do not by a base model. Reason being is that the base will likely have 3.73:1 gears and 1.25" torsion bars and weak rear springs. Whereas the Z-71 and NFE will have 4.10:1 gears (which will carry you up through a 33" tire), stiffer rear springs, and thicker torsion bars. Why NFE over Z-71? I have found the torsion bars in my old NFE are 1.35" vs the Z-71 at 1.30". It doesn't sound like much, but it equates to a 23% increase in spring rate - meaning it's a bit stiffer and will handle it better when you start adding the weight. The NFE also has an engine block warmer - a bonus if you live in cold environments.
First things to address: Tie rods - stock are anemic, get a set of Rare Parts. Shocks - the Eibach Pro Truck Sport shocks are an excellent value and were actually designed on my Avalanche loaded for overloading and traversing Death Valley. So - you get a purpose built shock for your rig with an off the shelf price. Tires - my preference is for the General Tire Grabber X3 because I get into a lot of stuff where I feel more comfortable having the thicker tire. A solid choice is the General Tire Grabber ATX. Can't go wrong with BFG KO3 either. If you have no gear and just want something inexpensive to try it out - pickup a Napier Sportz tent made for the Avalanche and the air mattress (fits the bed. It's a pretty cool little setup - I had it for a few years. Add a second battery. Find a NOS GM batter tray - it fits near the passenger side firewall, battery and isolator. wire it up and now you have something to start running your accessories to and can also jump start yourself if needed. Pickup some basic recovery gear - MaxTrax are a great thing to have along. There are ways to wake the engine up - but that is for a later day. Your transmission is a failure point - either get it addressed by a shop that understands the design flaw or at a minimum - make sure you have a big transmission cooler routed outside of the radiator to keep the temps down. Any questions feel free to ping me. Good luck - the Av is a great vehicle.