Minor nitpick, but I think Family should be split up - you're usually not really supposed to have any Pokémon only available by breeding (in nearly every case I know, every basic Pokémon/Pokémon that can hatch from an Egg that's in your region is available somewhere - this is why we have things like Unova's weirdly high evolution levels lategame, because Game Freak was careful not to make any of the Pokémon evolve before you can get them). Depending on the game, baby Pokémon are sometimes an exception, but more recently, even they have started to be universally available (whether in the wild or as an "only one" from an Egg or something). There are some weird cases like Zorua being unavailable in XY when Zoroark is just a normal encounter in Winding Woods, but they're definitely extremely rare in any case, and Zorua in particular went through the last Generation as an event Pokémon and then a gift Pokémon, so not exactly an ordinary case anyway.
Meanwhile, Pokémon only obtainable by evolving are perfectly fine and are actually really common in canon, especially fully-evolved third stages (Pokémon that have evolved twice) or evolutions of gift Pokémon (for instance, the Eeveelutions and Porygon2/-Z have never been in the wild).
This aside, here are my thoughts:
Common, uncommon and rare can be arranged however is conducive to good gameplay - there are only so many encounter slots per area, so I would lean towards the majority of your Pokémon being uncommon, with a few common species that recur especially often and just as few rare species that don't recur at all. In particular...
Super Rare - these should be really unusual. In most games, there are only a few of these or even none at all, and that works best (I would have maybe three of them, especially if they're new Pokémon/Fakemon rather than returning species, and especially no more if they evolve, because at that point you're just locking even more behind it). A lot of people complained about how rare most of Sun and Moon's new Pokémon were, to the point that they would be missed entirely by most players and were unreasonably difficult to use on a team; this would suggest that such an arrangement is not ideal. You don't want to make too much of your region this hard to get, and you especially don't want players struggling to get your Fakemon in this way unless they're really special like Mimikyu or Jangmo-o; in most in-game locations, anything less than a 10% encounter rate is a red flag. I would keep these to a minimum.
Ultra Rare/"Only One" - all starters; most fossils; sometimes Eevee, sometimes Lapras and sometimes Porygon, but any one of these can be made available in the wild as the developer pleases (usually pretty rare or otherwise special); and then usually one new line every region (Snorlax, Sudowoodo, Castform, Riolu, Zorua, Kalos had none of such, Type: Null unless you count it as a Legendary) that are generally retired from this status after the one Generation, (usually rare or super rare instead); any Legendary or Mythical Pokémon, except the Cosmog line and any future evolving Legendaries like it, of which there should be multiple but which still should be limited in number. As an actual percentage, this varies quite drastically in official games and I can't say I have a preference, so I would just treat these as "tack on however many actually work for your game." This is going to be different for everyone, really - a project with a lot of Legendary Pokémon can have as many as it needs if they're all addressed properly and not out of nowhere (SM did it fine - they all had some involvement in the plot; B2W2 did it remarkably - there was not only buildup to most as a collective, like the Ultra Beasts and tapu in SM, but to individual Legendaries with their own sidequests, like the Strange House story for Cresselia and the main-game buildup to Heatran in Reversal Mountain before you actually got the Magma Stone for yourself; ORAS did it terribly - they were bogged down, indistinct, unexplained and no effort went into finding them, only catching them, which was more a chore than a challenge). Know your limits, know how much focus or involvement you can afford to give, and your Legendaries ought to flow naturally - the only games that really mess this up are ones that go out of their way to fill a quota, so that's inherently the opposite of what you should be doing.
