While bouncing I have used a single component of my skill set actively - clinch wrestling (or Greco-Roman if you will, but I only ever trained Freestyle). Every single altercation I handled by clinching, holding and talking to the trouble maker until they settled down.
I kept other things in mind, and adjusted specifically how I did it to account for strikes. I would take a grip that's sub-optimal for throwing but quite good for preventing knees or punches from being thrown, so I wouldn't suggest exclusively training wrestling, but it should definitely be a significant component of your training.
Based on observing other bouncers who used different strategies, and talking to more, some of which used the same or similar strategies, I'd say it's a very good path to take. The clinch isn't that threatening of a position, and if you're short staffed and working alone, you don't want your troublemaker's friends getting concerned about his well being and dogpiling you. If you're clinched and talking to him, telling him to calm down, his friends have a very good option in supporting you, telling him to calm down as well and taking him away.
Most of them when they're sober will also realise they were being assholes and appreciate that you handled it with the minimum amount of damage necessary. They're less likely to cause trouble in the future, and the next time something goes wrong, they're more likely to be among the clear heads who support you. I've found this a couple times, and that's been repeated by other bouncers I've talked to who used the same approach.
It's also very good for dealing with the police. You don't spill any blood, you didn't throw any strikes. There's really no reason for them not to take your side. You're doing your job and doing it well. You're not going to get criminal charges pressed for overuse of force (that could happen if you knock someone out and seriously injure them in the process), and there isn't much in the way of standing when it comes to civil suits either.
As far as passive skillset goes - boxing, or more importantly head movement and blocking. The most common type of attack you'll see that isn't some form of grab will be a punch to your head. You want to know how to not get hit. For that you need to practice a style that does full contact sparring, that includes punches to the head as a significant component and teaches good defense. Knowing how to clinch off someone else's attack is also very useful.
Boxing, Muay Thai, San Shou are all good options for this, as they have the requisite qualities. Something like Kyokushin Karate or WTF Tae Kwon Do unfortunately isn't, due to the absence of head punches in the competition rules, and therefore the very high likely hood of their absence in sparring as well.
Clinching and blocking/head movement will be the bread and butter skillsets for you as a bouncer, they're the first things you'll want to learn well.
Also, if you're not already big and strong. Correct that, at least the strong part. Lift heavy weights. I didn't focus on strength training much before starting bouncing, and I handled things OK anyway, but everything would have gone a lot better had I been stronger. When you're stronger, whatever you're trying to do, you can do faster and easier.
As far as supplemental skill sets go - throws, leg kicks and body punches are good to have in your arsenal. Head punches have problems - you can spill blood, cause concussions and break your hands. None of those are desirable for a variety of (I hope obvious) reasons. You could do some damage with a punch to the body, perhaps breaking some ribs, which could be a pain to deal with later, but there's plausibility in stating that you only did what was necessary, particularly if you refrained from attacking the head. Leg kicks you're a lot less likely to break anything, but you can cause a good Charlie horse, and making the guy limp for a bit when he's the aggressor isn't going to land you in as much hot water. Similarly, throwing while it can cause damage, there's plausibility that you were trying to handle the fight with minimum damage possible, and forcing an aggressor down to the ground to gain control over them is a well known an understood tactic.
I'd suggest using chokes and joint locks as a last resort. If you don't cause any damage, it's not so much of a problem, but if you do, that really won't look good if you have to defend your actions in court. Particularly since chokes are banned for police officers in a lot of jurisdictions - if they're not allowed to use chokes but are allowed to use guns, you really don't want to be frivolously doing that.