This has been my experience:
Usually, I'll start by working with a set of dedicated Weapons tracks so the guns don't gum up the other fx edits. This all depends on the film's context though.
If its a walk n talk with one or two gunshots through the whole film, I'll cut them up in the regular FX tracks and run with no weapons tracks. But if it's something crazy like Blackhawk Down style, I may want to go wider so that I have many more Weapons tracks dedicated in groupings to Close, Mid, and Distant fire. The key with gun fights in my experience is that organization and compartmentalization are your friends.
Hi Mid Lo could be a good way to think about the anatomy of a shot, or in terms of Boom, Crack, shell eject (depending on gun type), LFE. And, I like to keep the amount layered edits for a gun to about effects 3-4 per shot - any more than that I usually print down to "splits" based upon their frequency content so as not to marry a sound that has a deep boom with a high crack. Then these will get region group and named something like "Jake Pistol Shot", and that entire region group will be duplicated as-needed for each shot. What I learned from a colleague is that about 1 in 10 gun shots should sound slightly different, like a pitch change of one of the crack elements or shell eject elements by a few cents - that way there is some variation but its subtle. Most of the overall gunfight variation we hear is the whiz bys and ricos so the gunshots serve as more a constant in the vain of percussives that keep it grounded.
For your three seperate shooters, it would be advisable to keep them dedicated to the same tracks through the sequence so that its very easy to see who is who, especially for the mixer- "checkerboarded" would be a good term for it
Regarding the sync of the shots, I usually sync the transient to 1 frame before the visual bloom because of the perceived lag time between audio and visual (in the same vain that even the best Foley artists are about 1 frame off because of lag time). And sometimes you want to cheat the sounds of shot to follow a certain rhythm, or not the follow a certain rhythm. It all depends on context. If you see a closeup of a guy firing 3 single shots from an assault rifle, each three must be cut to sync. But, if its a barrage of guns going off, and you have offscreen moments where you don't see the gun, that's where you can get away with playing more to the rhythm than the hard and fast visual.
Good luck! Gun fights are fun, but they can be overwhelming on the first run at it.