SIRvive, welcome to the forums. Lots of information here. I think you may find it a bit overwhelming.
As for your question. You have a few decisions to make. First off, since you have an EB, you most likely have the air ride suspension. If so, no one makes a lift kit for your suspension. So, you are now left with 3 decisions. You can 1) remove the air ride suspension and then go with a standard suspension lift, 2) go with a body lift, get 3 inches of clearance and that will let you clear 35's, or 3) go custom which is going to be big money.
If you go the standard suspension route, the conversion is pretty easy and a lot of members can tell you down to the part number the parts you will need. But, as your truck gets older, fewer and fewer companies are making lift kits for the truck. The only active manufacturer right now is Fabtech as I recall and they make a 6" lift for the truck (only for the standard suspension, not the air ride). But, plan on spending about $2000 for the kit and then another $600 or so to have it installed (unless you install it yourself, then plan on a whole weekend doing it, TRUST ME!!!!! I installed mine). The other big name that you will find for lift kits is Rancho. There's is a 4" kit, but they stopped making them a few years ago, but you can occasionally find them for sale.
I have installed both and while both are quality kits and allow you to use your truck to its fullest, I prefer the Rancho kit for 1 main reason. That would be the upper control arm ball joints are at a better angle than the fabtech kits. This will allow you to have the ball joints last longer.
With the body lift, you can fit 35's on the truck with no issues as long as you keep the rim width down. Going with say an 8" or 9" wide rim, all should be good. But, you decide on a 10" rim and you are likely to have issues. This assumes going with a 12.5" wide tread pattern.
Just to give you an idea, with the 4" lift (which is what I am running), I have managed to fit 37x12.5's on my truck and am able to go from full suspension droop to full compression with no rubbing. But, I have a very specific setup and changing even one thing will end up with major rubbing. I have also had to modify a few things to make it all work.
So, what you are after is a popular setup and you do have options. Question is what are you willing to do to get the setup you want.