Thanks, rruff. Your suspension mods posts are good reading. Appreciate you sharing your hard earned (and paid for) knowledge.
Ha! I haven't even put the camper on the Tundra!
I have a ton of experience with 3 setups on a '84 Toyota 2wd PU with terrible ground clearance. The only upgrade was an add-a-leaf (I was poor then). I bashed and barreled over rocks for 13 years and 170k miles, and the bottom of it was covered in dents and craters (including the oil pan and gas tank). I would traverse rocks piles and climbs that I had no business on... just get a running start, slip the clutch, and bam bam bam. Did it all the time. It never left me stranded, but that was due to miraculous good fortune rather than sound judgement... ?

As far as on-road handling goes, it was totally fine with the 2nd setup (a sit-up height shell), but it was pretty awful with the big stand up camper I built later... although offroad it seemed fine. So long as you aren't doing stupid stuff at the same time, even a tall camper can tilt sideways about 45 degrees before it falls over... which is a lot, believe me! Terrified my girlfriend, but I wasn't close to disaster. I wonder how it would have been with a spring and shock upgrade, regear, better tires, etc... but I'll never know.
So my recommendations are mostly based on lots of reading and pondering, rather than personal experience that I'd advise for anyone else! Except for maybe... reaching for "perfection" isn't really necessary... just drive within the limits of what you have (or exceed them?), and hope for the best.
Now to your questions.
Ground clearance. Bigger tires raise everything, including the diff (or diffs if it's a solid axle front). They also roll over bumps better. And wide tires will hold more weight at a lower pressure, which is nice. The downside is fitting them in the wheelwells, the price, braking performance is reduced a bit, there is usually an MPG hit (though not for the tires I bought), and the fact that they raise your gear ratio. Any of these may or may not be important depending on the specific truck and its specs. My front shocks are set to 2" lift and I plan to maintain that with a load, and keep the rear at stock height, so it will be level. It was not hard to make enough room for 35x13" tires. I have 12" clearance at the bottom of the diff which is the low point. My '84 was probably half that!
Good armor is another option (skidplates, sliders) although I don't have any experience using this as a substitute for clearance. I do have a skidplate, but nothing else in this category.
Shocks. I'm really pleased with the Ironman shocks and I think they'll be good with a big load as well. They are in the "digressive" valving category, which means they have relatively high damping at low speed piston movements (like you'd encounter in accident avoidance) but respond fine to fast motion like bumps. They are a little stiff on small bumps but that doesn't bother me. I took off the swaybar and was blown away at how well the truck handled winding mountain roads at speed, as well as rough winding dirt. Very planted and controlled. These are fairly inexpensive shocks and aren't available for everything. In the same category Dobinson and OME are options, but I think Ironman FCPros are better. A lot of people get 2.5" Icon, Fox, or King. These are very nice (and expensive), plus you can have them custom valved (Accutune does this for "free"). The downside for me is the that they require more frequent rebuilds (high pressure gas and light seals), and I plan to be living in my camper and don't want to mess with that.
Swaybars. My first try will be none. They specifically resist independent wheel motion, which causes more sideways jerking offroad... plus a lack of articulation. If I don't like the onroad handling with the camper I might try a rear one... the front is definitely staying off. If you have digressive shocks with high damping, they do well at sudden maneuvers. On sweeping turns you still get more body roll though, without the sways. I plan to just slow down if necessary... no big deal.
For rear springs I'm planning to add two leafs (one long and one short), and use either long travel airbags or cradles. The bags will mostly be for sideways leveling and fine tuning the height, not much load. Hopefully I'll get the damn camper on in a couple months so I can see how it does.
Good luck!