Okay, I went back and tallied up "votes" for each of the mentioned sets. Both in this topic, and from the
official custom moveset project posted by Amazing Ampharos. Here's what I ended up with, assuming I tallied everything correctly:
2332: 6 votes. Most popular set.
1313: 4 votes.
2313: 4 votes.
1333: 3 votes.
2212: 3 votes.
2223: 3 votes.
2233: 3 votes.
2312: 3 votes.
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2333: 3 votes. 4 positive, 1 negative.
1311: 2 votes.
1312: 2 votes.
2232: 2 votes.
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1113: 1 vote.
1332: 1 vote.
2113: 1 vote.
2323: 1 vote.
1322: 0 votes. 1 positive, 1 negative.
I have made two lines between the most popular sets from the rest. Green sets are most likely going to stay. Yellow sets need to be called into question, and decided upon if they should be a part of Mario's main sets. Red are, unless proven otherwise, currently not valid enough to be a part of Mario's main sets.
From here, there are a couple of things we can do before finalizing our sets. But I am going to start off by talking about the sets themselves.
2332 is easily the most loved set. Versatile, strong, racks up damage well, doesn't sacrifice much recovery thanks to Gust Cape, and overall seems to be one of Mario's best sets. It is staying for sure.
1313 is one of Mario's most popular default Fireball sets. Boasting two edgeguarding options, and having his best OoS option. Overall this set is very defensive in nature. Therefore, I have decided to re-add it to the list of Mario's sets.
2313 is very similar to 1313, and just as popular. Having mostly the same strengths as 1313 and only trading the type of Fireball you use, I feel as though both sets have earned a place to stay.
1333 is Mario's other most popular default Fireball set. Said to be great against King DeDeDe and Link by A2ZOMG, it has two edgeguarding options and trades recovery and a better OoS for more raw damage and KO power instead. I can see this being good against heavy/large characters that rely on projectiles, although there aren't many of those in Smash 4. I feel as though 1313 has more synergy when comparing the two, however. But if people want this set to stay, it can.
2212 is one of my preferred sets. The set itself is essentially a straight upgrade from Mario's default set in most matchups. With Scalding FLUDD's ability to rack up damage, combined with Shocking Cape's ability to score KO's, it is extremely versatile. You also have access to Mario's best OoS option, and Fast Fireballs for long-range pokes. This set aims to be effective in all areas of combat, only having a slightly weaker recovery due to its lack of Gust Cape.
2223 is a controversial, niche set. But it aims to be effective in an area that no other set can replicate. With the combination of HP FLUDD for pushing people off of the stage, and Shocking Cape + Super Jump for edgeguarding, this set allows Mario to go very deep offstage and net KOs that would otherwise be impossible for him. However, it comes with some huge costs: losing combos, an OoS option, loses a hitbox when trying to recover, and relies a bit too much on Shocking Cape. Not to mention, Mario's general set of tools don't really put the opponent in a good enough position to even use Shocking Cape most of the time. Despite all of these things, it seems decently popular, and it could potentially be Mario's best set in certain matchups, though this has yet to be proven.
2233 is similar to set 2223, but focuses much more on stage control. Able to trap opponents near the ledges of the stage with HP FLUDD, and then having two finishing options in either Shocking Cape or Explosive Jump Punch, this set is definitely powerful. It is also similar to the most popular Mario set, 2332, but sacrifices recovery for more KO potential. This is one of Mario's worse sets in regards to recovery, so be very careful, and stay on the stage as much as you can.
2312, like 2212, is essentially a straight upgrade from Mario's default set in most matchups. However, the small difference in your choice of cape is actually pretty big. With this set, you have more recovery than 2212 and you also gain a gimping option. However, unlike some of Mario's other popular sets, 2312 trades KO options and and having a specific gameplan for scoring KOs and instead opts for versatility and defense. It lacks two gimping options compared to 1313/2313, and it lacks Shocking Cape compared to 2212. This means that it has to rely on Mario's sup-par KOing options in order to win, just like default Mario. However, if you play your cards right, you can wear your opponent out enough to make them vulnerable to these options, as this set's defense is where it shines.
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2333 is a set that is popular, but unlike its brother set 1333, it seems to lack a solid gameplan when compared to it. It has two gimping options and a KO option, but like set 1333, I don't think the set has much synergy. And unlike 1333, it seems to lack the type of Fireball which would be essential for at least two of Mario's matchups: Link and King DeDeDe. So, despite being popular, I have decided to call this set into question. Is it really worth having both sets? So far, it seems like we might be better off keeping 1333 instead, but I will leave this up for other people to decide. Either way, it has been removed from Mario's list of sets for the time being.
1311 seems to be valuable in regards to countering Little Mac and Ness. And it seems to have enough points in its favor to warrant needing a set. The only thing that holds it back are popularity, and if 1311 is really necessary if we are going to have 1313 as a set. However, the longer range and faster charging time do seem to make it more useful than 1313 for these particular matches. What I wish to know is what other people would prefer. Either way, this set seems useful enough, so I will add it for now.
1312 is a brother set to 2312, having similar strengths and weaknesses, only differing by your choice of fireball. The only thing it loses out on is popularity, as Fast Fireball is more popular than the default. So it faces stiff competition from it. Additionally, Fast Fireballs are arguably more defensive than the default fireballs, and default fireballs only seem useful in certain matchups. Particularly ones where you don't wish to be on the ground against your opponent. And, so far, this has only been mentioned for the Little Mac/Ness/Link/King DeDeDe matchups. And for Little Mac and Ness, set 1311 tries to cover for them. So this sets faces competition from both sets 2312 and 1311. Which makes me unsure if it is warranted or not.
Lastly, set 2232 is similar to the popular sets 2332 and 2233, but it offers an interesting niche that the other two don't quite replicate. Raw damage, on all fronts. With the combination of Scalding FLUDD, Explosive Jump Punch, and Shocking Cape all in one set, this set has the highest damage output and KO potential out of all of Mario's sets. Making it a scary force to be reckoned with on the stage. I say on the stage, because like set 2233, the recovery on this set is very poor. However, I like this set, and I believe in this set's potential. It is the only set that combines both Scalding FLUDD and Shocking Cape, and while it loses out on recovery, it is probably the one set that will surprise people the most in regards to Mario's KO potential. Therefore, I am adding it to the list, despite (seemingly) not being as popular as some of the other sets.
So with all of that out of the way, here's what we have now:
Mario
1311*
1313*
1333
2212
2223*
2232* (only due to little representation/popularity but is otherwise good)
2233
2312
2313
2332
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1312*
2333*
Sets marked in asterisks are up for the debate. The other sets, as far as I am concerned, no longer need to be discussed in regards to their popularity or validity.
What needs to be discussed:
1311 vs 1313. Are both necessary? 1311 seems to have the edge due to countering Little Mac and Ness.
1333 vs 2333. Are both necessary? 1333 seems to take precedence over 2333 so far.
2312 vs 1312. Are both necessary? 2312 seems to have the edge in defense and synergy.
2223 vs default fireball sets in particular. Is it work risking a potential set, albeit a very niche one, over a default fireball set which is bound to be more popular initially? Honestly, I would wait to see 2223 in action before completely debunking it myself. However, a good portion of people also want more default Fireball sets, and I don't want to ignore their opinions either.
New sets to explore? We seem to lack a set that has both the default Fireball and Shocking Cape. Would anyone like a set like that? What matchups would it be useful in? What characters would it potentially counter?
Example sets being 1212, 1213, 1232, and 1233.