If we choose them based on their numbers and try to check each gen by popularity and fame this is what I'd choose:
Gen 0: Sora, Suisei and Miko are all solid.
Sora is the Mario of the company, the OG, the most basic and the true idol representative.
Suisei and Miko are both very popular and big.
Gen 1: Fubuki and Haachama
They are both very well known and with good numbers. Fubuki was the face of the company for a while, and Haachama is one of the most well known members of the entire company, she was trending non stop during her previous couple of years.
Gen 2: Subaru or Aqua
Both the biggest members of their gens, most recognizable. Aqua has gone inactive tho, but she used to be quite big. Subaru is currently bigger.
Gamers: Korone, very easy, she's by far one of the most well known, successful and beloved Hololive members.
Gen 3: Marine or Pekora, they're both near the top of the Hololive tier list, very big numbers, successful, famous.
The next 3 gens only have one contender, they just seem overall like the most popular at the time
Gen 4: Towa
Gen 5: Botan
Gen 6: Sakamata
However I think this way of choosing characters is kinda boring, for a game you should consider what every character brings to the table, how they can interact and balance each other.
Consider their themes, their character kayfabe, what sort of options they could have.
Like if you chose Botan obviously you'd want someone with a lot of military weapons right? So she'd likely be a zoner. So your game has that covered. If you chose Ayame you'd have someone that obviously has access to swords, so you have that covered.
Someone like Luna is often portrayed accompanied by her lu-knights so you could make her some sort of summoner character thus covering that option.
With someone like Haachama her duality is a big part of her character, so you can make her a character that can swap like Pyra/Mythra.
What about a pet or puppet character? That's also a popular archetype, now you have to consider who could fill that role.
What about a glass cannon combo rush down character? Well, you have to think of one too.
What about a trapper? Well, Marine being a pirate could summon a canon, or drop an anchor, or throw dynamite. So she could fill that role well.
Then there's Noel, a big bulky heavy knights, obviously that could be one of your slow but heavy hitting characters.
What about an agile and mobile brawler? Not really sure who'd be the best for that role, but now that's an archetype that needs one character to fit.
