How Many of Each Species (Ideally)...

Machamp, golem, tyranitar, dragonite/gyarados are good enough if 3 - 4 each

i would max out ttar golem machamp dragonite zapdos.

Machamp 2-3
Rhydon 2 (ground)
Golem 2-3 (rock)
Dragonite 1-2 (outrage), 1-2 (hurricane)
Tyranitar 2-3 (stone edge), 2-3 (crunch)
Vaporeon 1 (hydropump), 1 (aquatail)
Jolteon 1 (thunderbolt) 1 (discharge)
Flareon 1 (overheat) 1 (flamethrower)
Espeon 1 (ZH/FS) 1 (C/FS)
Alakazam 1 (PC/FS) 1 (C/FS)
Gyarados 1 (B/HP)
Gengar all SC/ShB, if not H/ShB
Zapdos 1 (thunderbolt), 1 (zap cannon)

Tyranitar 2
Dragonite 2
Rhydon 2
Machamp 2
Golem 2
Exeggutor 2

There are mostly more than two good counters against each raidboss, so you can go three deep with two of each. In case you don't habe 6 great counters just fill out with Dragonite.

For Tyranitar for example I would use a Poliwrath after my two machamps, but I would.not consider him a must have, so basically with those mentioned you take the best counter plus dragonite plus two of what you have available.

Most used:
3 Machamp
2 Dragonite
1 Jolteon
1 Double Grass Exeggutor

I use the above (or a subset of it) to fight every gym. No exception.

Others are optional.
1 Dark Tyranitar
1 Fire
1 Psychic

For occasional uncomon gym choices like Steelix, Mul, Machamp, etc.

No Rhydon or Gyarados, thanks

I only max 1 of each species because I want to use a variety of pokemon.

I have 1 of each as specialist powerhouses and an army of Rhydons that do everything for me. So many Rhydons in fact that I have only revived 10 of them since the gym rework for raid battles. They take down gyms and beat level 1-4 bosses. I swim in rhyhorns in my area, is what I am saying. Everything else is super rare. I was lucky enough to evolve my first Dragonite a day before DB/DC became legacy after walking 400 km with it.

Power up/max a maximum of 4 dragonite/tyranitar. Next on the list, machamp and golem (3 max of each). I wouldn't invest in more than 1 good mon for the rest of species

Machamp - I have 4 between 30-32; are enough
Rhydon - I have a 38.5 one; I need 0.
Golem - 3 maxed, 2 level 30; need 4th maxed for trying to solo Flareon
Dragonite - 3 low-mid 30s - enough for now; I will reconsider if Dragonite became a raid boss
Tyranitar - 2 SE low-mid 30s/want 6 Cr for Mewtwo; until then more than enough
Scizor - 2 lvl 30; need 0 for now
Exeggutor; one BS/SoB maxed, 1 lvl 32 Ex/SoB, 3 legacy double psychic at lvl 30; more than enough
Vaporeon - 2 38.5, 1 38, 2 lvl 30; for old time sake; don't need them now :(
Jolteon/Zapdos - 1 lvl 31, a lot 28-30, lvl 20 Zapdos; I'm good, don't use them now
Flareon/Moltres/Charizard/Arcanine - several of each at lvl 30/ want to max a Moltres
Lapras/Articuno/Jynx/Cloyster - 1 lvl 30+/lvl 20/lvl 20/5 lvl 30 - enough for now; 2 lvl 30 Piloswine also
Gyarados - 2 lvl 37.5 - don't use/need them now (odd HP Lugia if I remember them, but I usually forgot)
Alakazam/Espeon - 1 lvl 30 legacy, 1 lvl 34 C/FS / 2 lvl 30 - good enough for solo Machamps
Gengar(specify with or without Shadow Claw) - 1 15 attack lvl 34 SC/Sball, 1 perfect lvl 33 hex/Shadow Ball - used for solo FB Ala and now to start Lugia raids. Waiting for Mewtwo, I will see then if worth powering up a 3rd one

+

1 Maxed Lick/HS Snorlax I used as anchor for Articuno and sometimes for Lugia (before I knew I can rejoin mid battle)