I would say nothing would beat a selectable locker when it comes to offroad/durability, but we all know those will be the most expensive option.
Lunchbox types are noisy and won't be as strong but they are budget friendly if you are willing to put up with the rachet in the rear end.
Full on LSD's aren't really mean't to be offroad and will wear quicker that way due to the loads but they are street friendly in snow,soft terrain/street I would say they aren the second cheapest option, if you dont mind rebuilding it 30k miles after depending on abuse, also depends on wheel size the bigger, the less it will last.
The detoitTrue tracs would be the sweet spot of both worlds, they are not as cheap but they don't need to be maintained or need any friction modifiers, I believe this are what they call torsen carriers if I'm not mistaken, they also work better with reg dyno than synthetic but you can still use synthetic. Although it can be tricky if you get a wheel in the air, that's when you do the whole brake trick. Overall pretty solid choice on/offroad, I got one of these in my shopping cart for when I blow the g80 I reinstall in my truck about a year ago, as I plan to do on off road driving more often, would be nice to be able to lock at speeds higher than 20mph.
Automatic lockers are out of the question I'm sure you know what I mean with the lovely Gbomb posi. They are for low speed traction if not they jihad your rear end.
If you do a lunch one you wont need to re adjust the backlash, if you choose any of the others where the carrier needs to be swapped you would need to adjust the backlash, just make sure you check the original backlash from the old carrier before installing the new one and get new shims. Unless if by pure luck you end up with the same backlash/and can't pull the carrier by hand, if you can you need more preload, but enough rambling.
