Let's face it: The only real way to gain ground clearance, especially under critical components such as differentials and transfer cases, is by installing taller tires. The main purpose of suspension lifts is to give you room to run larger tires. Yet many times lifts introduce off-roading negatives such as spring rates which are either too firm (less flex) or too soft (excessive weight shifting), and a center of gravity which gets pushed too high (limiting climbing and sidehilling abilities). We've seen highly modified vehicles fail on obstacles (such as Dump Bump in Moab), only to be embarrassed as a stock flatfender on street tires drives right up and over!
Choosing the correct tread pattern and rubber compound for the surface you'll be traversing is important as well. Tires made from softer rubber get better traction though they wear out quicker. Treads with more sipes generally do better on hard or slick surfaces while bigger lugs and voids permit better self-cleaning and progress in mud. Big lugs also help in silt or sand if the tires have good flotation. Tall, flexible sidewalls help as well so don't even get us started on the new low-profile look. Ugh!
The single most important performance aspect of tires is correct air pressure. Too much air reduces the tire's contact patch, thus minimizing traction. Too little pressure allows tires to pop off beads easily, and reseating them on the trail gets old after a few times. Bead-lock wheels were developed specifically to keep that from happening. There is no single, magical air pressure that works for all drivers, trucks, and tires. There are too many variables such as vehicle weight, sidewall flexibility, type of terrain, and how fast you like to drive. Experiment and find out what works best for your combination.
As far as lower gears, lockers, more power, and the other stuff are concerned, they all help, but you've got to have big tires. And next time you start a budget 4x4 project, start with taller tires first. Cut off whatever bashed body is in the way and go beater-wheeling with nothing but giant tires and low air pressure. Showing up the poseurs and wallet-jobs is great sport.