BB386 has a large shell diameter, meaning you can fit bigger bearings in BB. Bigger bearings=better longevity. Technically, you will have no issues of having any of the axles inside the shell given appropriate bearings size of BB, so check your potential BBs for an actual bearing size used - for example, SRAM is notorious for putting tiniest bearings possible in all of their shells regardless of the BB. In this case they could use same SKU for any of the BB they produce (it has to be Dub BB for BB86 = tiny bearings = shite, Dub in T47 = ok, but they have shite everywhere instead).
What Google tells you is generally correct. 29 and 30 mm axles are lighter but also could be destroyed quite easily due to seized bearings. I wouldn't consider stiffness as an issue, I am quite strong rider and I feel no difference between 30mm and 24mm without taper. If I were you I first looked into what crankset you want to install, as you are not limited by the shell diameter. If it's shimano, go for 24 mm, if Sram, go Dub. If you want some of the endless chinese Cybrei clones, pick whatever you want, Dub option is usually cheaper and Ti 24 mm is more expensive and heavier.
