Disclaimer: This post, unlike usual Pokkén Arena content, is written more personally and contains bits of my personal opinion alongside the advice, take as you will.
Before I get into other details it's important to note first of all that Pokkén's 3v3 mode is unique in the sense that you don't pre-determine your order from before the match starts. While your first picks are blind, your second and third picks are chosen after their preceding pick has fainted. This opens up the door more for potential team building and compositions as it means you have flexibility to adapt to your current circumstance. Also, the active Pokémon that just won the last round recovers 10% of it's max HP.
When building your team for 3v3 there are a few key things you want to consider:
It goes without saying that synergy and meter management was already a key part of the game, but is even more important in this format. You now have multiple Pokemon with multiple different charge rates and synergy benefits to consider instead of just that of your main. In addition, what's passed on between each Pokémon in terms of synergy meter is it's percentage ignoring character specific meter rates, meaning 90% off a Shadow Mewtwo would become 90% of a Mewtwo's bar upon switch in, this basically allows you to use faster charging characters as meter batteries for those who would otherwise struggle to fill their bar. This will likely become the main crux of everyone's team-building ideas as after all, having a full bar on the right Pokémon at the right time can quite literally win you a set right there and then. Imagine clutching out a game with Pikachu Libre, dealing a bit of damage to the second before falling and then passing over a fully charged synergy bar to a Charizard who can now run a complete pain-train from the get go. In a similar way, denial of synergy meter is now also very strong and can really turn the tide against a team that's looking to charge up. Weavile players rejoice, this is your time to shine! But i'll touch on that specific detail later on in Tailoring picks for what you're likely to see. There of course isn't an absolute need to rely on synergy, you shouldn't feel deterred from starting characters like Mewtwo who certainly won't build a bar in one turn if you feel like its the right way to kick off your game. But you need to be wary regardless that you're more than likely to be going up against characters looking to pass some form of a baton on so stay resolute!
Support picks and cheers
Support picks actually become a lot more interesting in this format because you're locked into only one for all 3 Pokemon meaning you'll almost certainly want to leverage as much out of your choice as possible. As per usual, picks like Eevee and Frogadier are very useful as the latter can provide backup and setup for almost anyone while the former giving a small recoverable hp boost and attack buff is almost always useful - especially if needed to nullify the light attack armour granted by burst mode. Mega Rayquaza also becomes a much more deadly weapon in the sense that one wrong move can spell the end of a vast amount of HP on a potentially crucial Pokemon to your team structure. I'm personally finding a lot of good use out of Sylveon and Croagunk right now as Sylveon provides me with crucial defence and recovery for pinches and Croagunk allows me to melt opponents down faster when I need to pull the trigger. As for cheers, while I suspect Support cheer will continue to see a lot of use alongside Standard and Special cheers, I think it's important not to sleep on Synergy cheer this time around since the initial boost to your meter in round 1 will almost certainly be a huge boost for players who want to build meter quickly. In fact, very meter hungry teams may benefit greatly from this cheer in particular. A team consisting of Lucario, Shadow Mewtwo and Weavile would have a field day in the right circumstances with all the meter they could amass, especially with a Jirachi behind them.
Adaptability vs Structure
Touching back to what I mentioned in the opening paragraph, this game gives you more control over the 3v3 structure than usual, you pick what comes next at any given time. With this in mind, do you build a team that has a very clear gameplan and picks that will always go first, second and third - or do you pick a team that is much more flexible in it's positions at cost of the ability to execute a perfectly conducted pain train? Or perhaps you plan for both, finding a gameplan that you can commit to if need be but adapt if things go south. My personal advice would definitely be to try and invest in a team that gives you options for multiple outcomes, this is why I expect to see a lot of Lucario in the upcoming format as he's one of the characters in the game that provides the most flexibility in what you can do with him - a one size fits all reliable rock who builds synergy easily, uses it like a champ but also simultaneously doesn't need to rely on synergy to be a threat either - making him a scary pick to throw out in any position on top of being one of the easier Pokémon to pick up and play with. But you may also find that a team built too much on bending to the situation may lack a clear identity and lose it's way against teams that are particularly bull-headed with executing their plans. Sometimes even if the strategy is easy to see, it doesn't at all mean it's easy to stop, the strongest structure won't fall easily. The choice is completely yours in this format and it's exciting to see what kind of things people will come up with.
Tailoring picks for what you're likely to see
This is perhaps the most interesting part of 3v3 as utilising flexibility here can really spell the difference between a match that runs smoothly and one that can go south quite quickly. I've harped on a lot about the synergy battery characters who are likely to lead teams and its for good reason - the meta is young and a lot of people are likely to stick to the base format of charging meter early on and having leaving a suitable care package for the last character to sweep with. You're far more likely to see the likes of Pikachu Libre out first than Gengar for example, similarly I can see a lot more players opting for Mewtwo as their last picks over Shadow Mewtwo who is a much more volatile pick to have as your last line of defence. Using basic knowledge and prediction, you can bolster your team significantly by playing around what's strong and what's popular. Weavile is a big power pick in this meta because he has the benefit of not only building synergy and support meter quickly but also being a strong denier of synergy from the opponent. Throwing in Weavile at the right time can really prove to be a disruption, the same can be said for other characters who have meter denial properties like Gengar and Sceptile to a lesser degree. Perhaps even Yveltal can see a return to competitive prominence as denial of burst meter becomes so much more of an issue on a Pokemon that's relying on it to survive. But I digress, If you know what your opponent is playing or likely to play and you can make a countermeasure for it, you're only going to come out much stronger.
Your own personal comfort!
Despite everything I've said so far, the most important thing is to be comfortable on what you're picking. You can spend however long it takes building a composition that you feel excels in this format but it doesn't matter if when it comes down to it and you need to pull through - you don't because you're uncomfortable on the picks. Because you get one HP bar and one only per Pokémon, you need to stretch every little bit of life you have to it's absolute limit. I personally don't think Suicune adds a lot to any fancy team composition in this format, but Legendary beast is my rock of comfort and stability, so that rock will certainly be grounding out all my team choices.
Closing thoughts and sample teams
I hope you guys have enjoyed the format so far and are looking forward to your respective qualifiers where we'll see the fruits of your labour!
This was a new kind of piece by me but one I'm hoping can prove helpful to a budding player wanting to mess around on the format. If you're looking to play the format online, various community members have 3v3 group match lobbies, as do servers like Pokkén EU, you can also ping for 3v3 friendlies in the main Pokkén Discord. Burnside has also graciously brought back his online tournament: Victory Road for a 3rd time, this time with the 3v3 format as well so be sure to check it out!
I also made a tier chart not too long along depicting where I thought each Pokémon would be mainly seen in turn order, as well as their reliability in general. Let me know if you agree or not if you check it out!
Pikachu/Gengar/Lucario (Jirachi/Support cheer) - Build synergy for Gengar, be Mega Gengar, finish the job on Lucario.
Darkrai/Weavile/Sceptile (Umbreon/??? cheer) - Disruption to pace and flow, trap based field phases as well as denial of synergy through built in mechanics and shield pressure
Shadow Mewtwo/Charizard/Blaziken (Mega Rayquaza/Synergy cheer) - Plus Ultra?
Pikachu Libre/Lucario/Decidueye (Frogadier/Standard cheer) - Ol' Reliable. Strong, flexible and stable picks into any situation.