I know this is a 2 month old bump.... however, here's some things to consider that I didn't see brought up, or saw brought up that really aren't exactly correct.
5.56 will underpenetrate structural members against all other types of weapons and ammunition save birdshot (which if you're using for home defense, please report to your nearest veteran for a prompt butt-stroking... wounding characteristics of birdshot even at close range do not make it a lethal selection versus ANYTHING other than birds.. in fact you're better off using .22LR)
I don't follow Cali law on a lot of things, because cali gun law specifically is best equated to a number of lewd jokes.
having said that, what are you more comfortable with. You're a Marine, but are you an 03xx? The reason I say this is that although every Marine a riflemen and all that, if it's not something you honestly have good, repeated, to the point of muscle memory training with... then what is?
A shotgun with loads for actual anti-personnel use (#1/0/00 buck or slugs) will out penetrate everything... especially with slugs, if you miss. It can happen, even to the best of us.
5.56 yaws and fragments easily, dispersing energy and reducing hazard for if you miss. One of the prime reasons that law enforcement has transitioned away from the ever-sexy MP5 is specifically because 9mm and pistol calibers in general will penetrate further than 5.56, which means that any operations they do have more hazard to surrounding innocents. It's a documented fact.
Pistols have the advantage of shorter length, however have a disadvantage of less stability in the firing platform (just your arms and maybe what you get to lean against to fire) as well as a shorter sight radius and barrel. Pistol ammunition has the detriment that due to common construction, hollowpoints will fill with structural material they pass through and then function like full metal jacket bullets, penetrating further due to bullet mass and velocity than originally intended.. even if they're subsonic.
Rifles and rifle caliber pistols (speaking specifically of any of the AR variants, especially the Sigs with the "arm brace) give you more to work with in terms of both service related muscle memory (if you truly have it) as well as better sighting options and overall carried round count. Then, on top of that they also have significantly more stability for being able to place shots where you need to due to being shoulder fired.
Humans don't just drop with one round unless it's to the dome. Anything other than central nervous system involvement is something that an assailant can fight through if they are so inclined due to motivation through mindset or medication. What this means is that you WANT and NEED to be able to put multiple rounds into whatever you have deemed to be a hazard to your life and the life of those whom you protect.
I've got shotguns, I've got rifles, and I've got pistols. My pistols are for the interim between when my german shepherd goes ballistic and attacks whatevers in the house, and I can get to my rifle. My home's designed in such a manner that I don't need to bother with clearing it, in fact I won't be. Let the cops do that. What I WILL be doing, is hard pointing in a specific location that's 3 steps from my bed, and anything I see from there? Well, it's their choice what happens. That point also allows for safety of my kid, wife, and neighbors due to orientation of the home in relation to it's surroundings.
My rifle I use is .308/7.62x51. I use high expansion rounds in my rifle to mitigate it's penetration capability for both residential construction as well as meat. My pistol's .45. Wife's got the same stuff albeit slightly less "pimped out". Those are the "go to" guns. The shotguns are configured and stored in readiness however aren't a primary go-to gun for anything. Here, have a picture of my party box.
Whatever you get, training is important because shot placement is paramount over caliber... 9mm works just as good as .45 unless you need a larger permanent wound cavity, and 5.56 especially at residential home ranges of employment is extremely devastating. All of those factors don't matter if you can't hit what you need to, repeatedly, under duress.
I also see that you got yourself a shotgun. Don't bother with a tri-rail. A surefire shotgun foregrip for the pump will suit your purposes perfectly while being comfortable to fire. I would also recommend looking into getting a side-saddle due to the ammunition-hungry nature of shotguns due to the size of the ammunition.... and doing loading drills. Loading drills. LOADING DRILLS. You need to know how to feed it, because you generally have as many or less shots with a shotgun than you would with a revolver... so knowing how to feed the beast is important.
If you can't take a shotgun class, look at the Magpul "art of the tactical shotgun" video for drills and techniques to try, and head out to the recreational range on post or one off post, or just a good patch of desert you can shoot at, and practice firing, loading, firing. Effective shotgun utilization is a lost art for the most part. You also want to pattern your shot you use for defense. Most homes you're not going to have much distance to actually get spread on the shot load, it's not like the movies where you can just aim it in the general direction and expect a hit.... but at the same time, there's a "maximum point range" for ammunition in shotguns... specifically, at some range that differs between shotguns as well as between ammunition FOR shotguns, all of your pellets will NOT hit a man sized target. You need to know that range, so you know where your grey area of "take the shot/don't take the shot" is, given your target, foreground and background. You're responsible for every slug, bullet, or pellet that exits that muzzle when you pull the trigger... and if 8 hit your bad guy and 1 hits little johnny in the house next door? A quote from FMJ in "the head scene" comes to mind... you're in a world of....