Solo, Duo, or Trio?
Trio
Trio is undoubtedly the strongest ratio, having more options and, thanks to having more DHCs to dump meter on, potentially even more damage than a duo at the cost of squishier characters. But if you don't have three characters that you like playing, you're only dampening your fun in the long run by forcing yourself to play a trio, and that's not optimal.
Duo
Duos are a bit weird in that their maximum damage potential is less than that of a trio's, and despite being tankier, a duo character can still be 2-touched, or even 1-touched by a trio team under the right conditions. But that all requires the trio to burn a lot of resources, while a duo needing less resets and less meter to kill in more common situations (such as at round start when meter is scarce) can make a huge difference over the course of a match.
If you want what's considered a "good" duo, then here is your checklist:
Do both characters support each other well
Do both characters fight well alone
If one of the above does not apply:
If the support is very one-sided, is the character that's expected to be on point getting great support to make up for it, and can the anchor at least fight well without a partner
Is it easy to switch orders without spending meter and keep your advantage (combo extending tags like Double or Painwheel, sliding knockdowns into tags and still being plus enough to run okizeme or setup for zoning)
Examples of flawed, yet strong duos:
Beowulf/Big Band being the prime example as solo Beowulf sucks, but Beowulf with Big Band is amazing and Big Band also gets good support
Painwheel/Double being another example as while Painwheel doesn't want to be solo, if Double is on point then she can easily tag to Painwheel mid-combo and continue it without spending meter
Robo Fortune/Cerebella being yet another case where anchor Robo is not a favorable position, but Cerebella can easily get a sliding knockdown from her combos then tag Robo Fortune in safely, even if you don't get a combo (though you can in the corner)
Fortune/Big Band's synergy is heavily one-sided in Fortune's favor, but both characters fight well alone and Fortune with Big Band's assists with the addition of a duo's health and damage is a major problem
If you don't care about any of that, play duo anyway because those are the two characters you like. It's very much possible to win even with "incomplete" duos.
Solo
Do you happen to like only one character in the game? Play solo. Solo Beowulf is a struggle, and Peacock certainly benefits greatly from having partners, yet these two have placed top 8 at the most stacked tournaments as solos. Neutral and defense can be scary, but your opponents will melt once you land a hit. At the end of the day, more options will outweigh having more health and damage, but sometimes said health and damage will scare your opponent into switching from a trio to a duo, or a duo to a solo to fight against you. This happens more often than you would think, even in high level play. It's really funny, and everyone in the room nods their head in understanding because nobody wants to root for the solo player, not even other solo players. I'm rooting for you, though. Don't let anyone stop you, but you.
Who are the good solos?
If you want a list of good solos because people keep blowing you off with, “All characters can work solo!” without answering your question:
Best solos
Fortune - Amazing matchup spread, gives the most popular characters a hard time even without an assist. Has very good defensive options both on the ground and in the air, metered and meterless. Headless is very much Fortune’s own assist. Undoubtedly the best solo character by a decent margin.
Fukua - Self-sufficient and versatile playstyle. Overall, a very strong character. One very nice thing about solo Fukua is that she can setup a shadow with her 214K specials mid-combo, activate snapback to recover red health, and then release the shadow to continue the combo instead of bringing in the next character.
Double - Another self-sufficient character who can change up her playstyle to fit the matchup.
Annie - Strong all-rounder with good solo mixups, a screen-controlling projectile to keep opponents from flinging certain assists at you, and good defensive options with her DP and 2LP. 2LP being especially good for challenging air-dash pressure. Can easily make a comeback if she gets the meter for Star Power, which will inevitably happen as the opponent whittles down her solo health pool.
Serviceable solos
Valentine - Also a great matchup spread that even assists may not cover for if your movement and ability to play lame are on point. Biggest issue is that her defensive options all require meter, and even then, they aren’t amazing. Having two air supers with one being hard to punish is better than what most characters have, though. She just likes having an assist too much. OutlawSpike has placed in top 8s with solo Valentine.
Peacock - Just a very strong character overall. Harder to keep opponents out, so you’ll have to really get your movement and close-range game down. Loss of easy access to Item Drop Loops isn’t the worst, but still a big loss. Good defensive options in her teleports, DP M Bang, and 2LK to stop instant air dash pressure helps her fight her way out (and with solo health she gets many chances), while her Lenny super helps her control neutral even as a solo. Ran by Psychopath, who has placed high in tournaments.
Parasoul - Same idea as Double and Fukua, but not as strong as an individual.
Filia - Your movement and reads better be absolutely on point because you’re not going to win by throwing out Filia’s normals and unsafe Hairballs. Wait for your opponent to overcommit to an action, then move in. Filia's mixup game is scary even when solo and she can erase a team in a blink thanks to her solo damage. Reis has placed in top 8s with solo Filia for several years.
Eliza - Some will say she's one of the stronger solos, others will say she has too many bad matchups. Neutral can absolutely be a struggle, and her lackluster defensive options and tall hurtboxes can leave her crumbling to pressure, but her solo mixup is strong enough to completely run a team over if she does manage to get the momentum she needs. Add on her Blood mechanic that lets her regain life, and you have a solo character that can heal half a trio combo's worth of damage off of every confirm.
Questionable, but doable
Big Band - Hardest hitting solo with the best defensive options in the game. Also has some of the hardest matchups in the game, so if your opponent’s team can play lame, you might not even get to play. His big size makes a big difference, and he still has to take a lot of risks. The “I made one mistake and lost a character” factor is very high, especially since he cannot be safe jumped when he has meter for SSJ, and his parry is always a threat that a Band with a solo health pool is more than willing to take a gamble on. Not as strong as Twitter and salty Discord messages make him sound like.
Cerebella - Similar to Big Band, while Bella is very solid on her own, some matchups will just not allow her to play.
Squigly - Her strongest neutral, pressure, and defensive tools are linked to meter that she can't rely on a battery character for, or stance charges that can be difficult to build in neutral against some teams without a partner to protect her. The former being more important than the latter, as getting a charge in neutral isn't all that difficult in practice, but her solo meter gain can't keep up with how much she likes to spend it. THAT SAID, EU player Bigtonney has been very successful with solo Squigly, but it’s an uphill battle, nonetheless.
Difficult to utilize their full potential
Beowulf - Can’t easily build Hype on his own, and he’ll spend it much more quickly than the time it took for him to get it. Has some very difficult matchups so sometimes he just will not be able to play. Even if solo Beo does manage to get in on the opponent, sometimes the right safe DHC will just send him back to square 1. iDante and Dudeguy M.B. have placed in top 8s in the most stacked tournaments (EVO included) with solo Beowulf. They are simply just better.
Umbrella - She can streamroll you if she gets a hit... like nearly every other solo in the game. Neutral is a struggle, especially against zoners, and she doesn't have another character to build meter for Retina Reflectors to create breathing room. Her poor defensive options especially do her no favors, so a good player will take advantage of that. The situation only gets worse if she tries to play in Ravenous, messes up, then gets stuck in Starving without anyone to help her out. On the other hand, solo damage makes it much easier for her to kill an opponent with her Feeding Time level 3, which makes it much easier for her to stay in Ravenous.
Painwheel - You’re gonna have trouble if you want to play aggressively, but if you play slow and patient you might be fine. The problem is you’ll have to gain the life lead for this plan to work so that the opponent can’t just sit back and let the timer run down themselves. Learn your Hatred Install combos. Defense can be a struggle as your best defensive options require meter… and you really want that meter for Hatred Install.
Robo Fortune - Meterless damage is low even with a solo character’s damage, and you don’t have another character to build the meter for you. Her mixup game is also poor as she has no assists to help her convert from grabs, and some of her overhead and crossup resets often have a starter that heavily scales the combo with multi-hits. Trying to form more heads in neutral means that you have to pause your zoning for a bit, which can be dangerous. Your defensive options are also trash. Be prepared to run around a lot and shoot a LOT of beams, but thankfully you can rack up a lot of chip damage to ensure the opponent can’t try to hold a life lead by laming you out.
Who Knows?
Black Dahlia - ....
Marie - .....
But of course, the most important thing is to play the characters you enjoy. Only like one character and they’re weak as a solo? Follow your heart and stick with them. Especially if you don’t care about reaching the top level. Or especially if you want to be the pioneer and prove people wrong.
This is not a character tier list. Team value is not something that can be ignored. Some characters need help to reach their full potential. Good solos do not necessarily make good anchors (See: Fortune, Valentine, as they are very selfish teammates. Eliza, who at one point was not considered a good solo, but always thought of as a fair anchor as her assists are good). I am not the right person to throw out a character tier list, though I’ve given you the knowledge to build a strong, competitive team IF you care for that, and avoid a disaster.