Properly using Mewtwos?

Since I got my first Mewtwo just over a year ago, concluding you don’t have a Shadowball Mewtwo. I imagine your options would be to have your best new one be ice beam or psychic. Ice beam would help against a return of Rayquaza/Latios/Latias.

Psychic could help you do some daily filler solo-raids (Machamp) that you may or may not be able to already easily do. I doubt Kyogre is coming back anytime soon, so I’d not factor in an electric Mewtwo.

My standards for Mewtwo have me pleased with 2250+, however don’t transfer any of them. Keep them to trade. I just traded for one with a new best friend and it went 2235 to 2253 w/o getting lucky (15a/14d/12). All of them are good to catch, have, trade.

I wouldn’t power up a whole squad of them. Think about two or three to a useful level, and maxing not necessarily needed for ones with these new moves. You should collect CTMs, too, so they and you can be more versatile.

You could max a focus blast mewtwo for those normal types in gyms, it'd save you potions, so if you have an excess of mewtwo candies, go for it. Ice beam and thunderbolt have their niches, that you may and may not have them covered. Psychic is also a good one for the machamp raids that you should totally grind if you dont have an army of them yet. Most stardust efficient way to solo it along with rayquaza, and mewtwo is just better. For psychic, i'd say pick your best weather boosted one(s) to save on candies, at level 30 it's a beast.

Sorry you missed the best moveset but Mewtwo is still a great option in some cases.
Definitely go either ice or fighting. But don't max, level 30-35 should be enough to get a lot of mileage out of your Mewtwo(s). Also, like devshaw said, power up your best one or two only. But not until you have traded your worst ones for other Mewtwo. You might get a lucky one or even a hundo.
Worry not, there is no immediate need for non-shadowball Mewtwo right now.

Wait until Mewtwo will leave raids, and power up the best one with Ice Beam, Thunderbolt to at least 35 lvl. Focus Blast is awful 1 bar option who usually do overkill on defender. Machamp and Hariyama do the job better. For Flamethrower, budget Flareons are enough and Legendaries and BB charizards are lots better.