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Next to "What size tire can I fit...?" I think you've posted the most frequently asked question on this board. Don't get me wrong, I'm thrilled to actually have a recommendation for you.
They're expensive, but I'd recommend the Rubicon 6.5" kit. I've recently installed their 6.5" on my 01 F250 4x4 CC shortbed w/5.4. I'm totally satisfied with it and recommend Rubicon.
I would have to go with fabtech or superlift. Both offer good quality lifts, and at reasonable prices. Both also offer a progressive spring pack to help out on the ride. Fabtech offers a 5.5" lift.. fits right in your 4-6" lift category
Rezvani's Latest Post-Apocalytic Monster Is a Ford F-150 Raptor Underneath
Slideshow: Called the Fortress, the 850-horsepower pickup combines Raptor underpinnings with military-inspired features, survival equipment, and a starting price of $285,000.