Base Stat Total is a blunt tool. It sums HP, Attack, Defense, Special Attack, Special Defense, and Speed and calls it a day. It does not care about typing synergy, abilities, or move pools. But if you sort every type by BST you get a pretty honest map of which mons the designers gave the biggest budgets to, and legendaries end up on almost every list.
I went type by type using base forms only. No Megas, no primals, no Ultra Necrozma, no Crowned Shield / Sword unless I flagged it. Each entry gets a one-liner, the generation it debuted in, and the shortest route to catching or evolving one today.
Normal
Arceus (720, Gen 4). The plate god. Event-only in the mainline series, obtainable via the Azure Flute event or Legends: Arceus post-game.
Regigigas (670, Gen 4). Sluggish and gorgeous. Catch in Snowpoint Temple in Diamond/Pearl once you have the other Regis.
Slaking (670, Gen 3). Truant ruins it, the stats do not care. Evolve Vigoroth at level 36 in any Hoenn or later game.
Silvally (570, Gen 7). The synthetic Arceus. Given during the Aether story in Sun/Moon after finishing the Type: Null questline.
Snorlax (540, Gen 1). Blocks roads, eats pancakes. Wake it with the Poké Flute on Route 12 or 16 in Kanto, later found in most regions on foot.
Fire
Ho-Oh (680, Gen 2). Rainbow phoenix, arguably the mascot of Gold. Catch at the top of Tin Tower in Gold/HeartGold once you have the three legendary beasts.
Reshiram (680, Gen 5). The white dragon of truth. Catch at N's Castle in Black, or Dragonspiral Tower in White 2.
Volcanion (600, Gen 6). Steam-powered mythical. Event-only, distributed for X/Y and Omega Ruby / Alpha Sapphire in 2016.
Heatran (600, Gen 4). Lava lizard bolted to the floor. Catch in Stark Mountain after the Sinnoh League in Diamond/Pearl/Platinum.
Blaziken (530, Gen 3). Speed Boost still terrifies. Pick Torchic as your Hoenn starter and evolve twice.
Water
Palkia (680, Gen 4). Space dragon, half Dragon-type. Catch at the Spear Pillar in Pearl or Platinum.
Kyogre (670, Gen 3). Rain-summoning whale. Catch in the Cave of Origin in Sapphire, or the Marine Cave in Emerald.
Manaphy (600, Gen 4). Egg mythical, technically breedable with Ditto for Phione. Originally distributed via Pokémon Ranger.
Suicune (580, Gen 2). Roaming, then plot-locked in Crystal. Chase around Johto in Gold/Silver, or catch at Tin Tower in Crystal.
Milotic (540, Gen 3). The reason old Contests existed. Evolve Feebas by max Beauty, or trade a Feebas holding a Prism Scale in Gen 5 onward.
Grass
Celebi (600, Gen 2). Time travel onion. Event-only across most generations, obtainable in-game only in HeartGold/SoulSilver via the Ilex Forest shrine event.
Shaymin (600, Gen 4). Land form is 600, Sky form redistributes those points. Received via the Oak's Letter event in Platinum, at Floaroma Meadow.
Zarude (600, Gen 8). Jungle mythical. Distributed via Pokémon HOME code with the CoCo movie in 2020.
Tapu Bulu (570, Gen 7). Bull guardian of Ula'ula. Catch on Poni Island's Ruins of Abundance in Sun/Moon.
Kartana (570, Gen 7). Origami sword, glassiest defense stat imaginable. Ultra Beast in Moon and Ultra Moon only, caught on Ultra Space wormhole visits in Ultra Moon.
Electric
Zekrom (680, Gen 5). The black dragon of ideals. Catch at N's Castle in White, or Dragonspiral Tower in Black 2.
Zeraora (600, Gen 7). Fast punchy cat, no evolution. Event-only, distributed for Ultra Sun / Ultra Moon in 2018.
Regieleki (580, Gen 8). Pure Speed on a stick. Catch in the Split-Decision Ruins in the Crown Tundra DLC for Sword/Shield.
Raikou (580, Gen 2). Roaming beast, first of the trio. Chase around Kanto in Gold, catch in the Burned Tower in HeartGold/SoulSilver.
Xurkitree (570, Gen 7). A pile of cables. Ultra Beast in Ultra Sun, caught on wormhole visits.
Ice
Calyrex Ice Rider (680, Gen 8). The horse plus king fusion. Fuse Calyrex with Glastrier using the Reins of Unity in Crown Tundra.
Kyurem (660 base, 700 fused, Gen 5). Cold husk of the original dragon. Catch in Giant Chasm in Black/White, then fuse with Zekrom or Reshiram in Black 2 / White 2.
Baxcalibur (600, Gen 9). The Paldean pseudo-legendary. Evolve Frigibax through Arctibax, level 54 in Scarlet/Violet.
Glastrier (580, Gen 8). Angry horse. Catch in the Crown Shrine in Crown Tundra by planting carrot seeds in the correct field.
Regice (580, Gen 3). Bug in the ice. Catch in Island Cave on Route 105 in Ruby/Sapphire, after unlocking the Regi puzzles.
Fighting
Zamazenta Crowned Shield (720, Gen 8). Steel/Fighting when holding the Rusted Shield. Catch as part of the Sword/Shield main story, form-swap with the shield.
Urshifu (650, Gen 8). Rapid Strike is Water/Fighting, Single Strike is Dark/Fighting. Evolve Kubfu after clearing the Tower of Waters or Darkness in Isle of Armor.
Keldeo (580, Gen 5). The fourth musketeer. Event-only, obtainable in Black/White 2 with an event Keldeo taken to Pledge Grove to learn Secret Sword.
Terrakion (580, Gen 5). Rockslide legend. Catch in Victory Road in Black/White after the story.
Conkeldurr (505, Gen 5). Grandpa with concrete columns. Evolve Gurdurr via trade in Black/White, or use an item swap in later generations.
Poison
Eternatus (690, Gen 8). Skeleton dragon that ate the plot. Catch after the final battle at the Tower Summit in Sword/Shield.
Nihilego (570, Gen 7). Poison/Rock jellyfish. Ultra Beast in Sun/Ultra Sun, caught during the Aether Paradise story.
Naganadel (540, Gen 7). Poison/Dragon wasp. Evolve Poipole after learning Dragon Pulse in Ultra Sun / Ultra Moon.
Gengar (500, Gen 1). Purely Poison in origin, secondary Ghost. Evolve Haunter via trade in every mainline game, or level 25 with Linking Cord in Legends: Arceus.
Toxapex (495, Gen 7). Impossible to kill in Gen 7 singles. Evolve Mareanie at level 38 in Sun/Moon.
Ground
Ting-Lu (700, Gen 9). Dark/Ground moose deer. Unlock the Ruinous shrines by collecting purple stakes across Paldea, then catch at the Groundblight Shrine.
Groudon (670, Gen 3). Half a continent. Catch at Terra Cave in Ruby, or the Cave of Origin in Omega Ruby.
Garchomp (600, Gen 4). Land shark pseudo. Evolve Gible through Gabite, level 48 in Diamond/Pearl.
Zygarde 50% (600, Gen 6). Snake mode. Complete the Zygarde Cell hunt in Sun/Moon to build a 100% form, or catch the base form in Terminus Cave in X/Y.
Landorus Incarnate (600, Gen 5). The one Kami people actually use. Catch in Abundant Shrine in Black/White after obtaining Tornadus and Thundurus.
Flying
Rayquaza (680, Gen 3). Sky serpent. Catch at the top of Sky Pillar in Ruby/Sapphire/Emerald.
Lugia (680, Gen 2). Storm keeper. Catch in the Whirl Islands in Silver/SoulSilver after obtaining the Silver Wing.
Yveltal (680, Gen 6). Death bird, half Dark. Catch at Team Flare Secret HQ in Y during the story.
Ho-Oh (680, Gen 2). Doubles here as Fire/Flying. Same catch as above, at Tin Tower.
Dragonite (600, Gen 1). The reliable orange dragon. Evolve Dragonair at level 55 anywhere Dratini shows up.
Psychic
Mewtwo (680, Gen 1). Test tube legend. Catch in Cerulean Cave in Red/Blue after beating the Elite Four.
Lugia (680, Gen 2). Included for its Psychic secondary. Same Whirl Islands catch.
Necrozma (600, Gen 7). The prism that eats the sun. Catch on Mount Lanakila in Sun/Moon after credits, forms unlock in Ultra Sun / Ultra Moon.
Deoxys (600, Gen 3). Space virus, form changes by region. Event-only in mainline, forms selectable at meteors in Emerald and Omega Ruby / Alpha Sapphire.
Mew (600, Gen 1). Original mythical. Event-only, obtainable in Let's Go via Poké Ball Plus, and via HOME transfer for most modern games.
Bug
Genesect (600, Gen 5). Ancient bug fitted with a laser. Event-only, distributed for Black 2 / White 2 in 2013.
Buzzwole (570, Gen 7). Ripped mosquito. Ultra Beast in Sun / Ultra Sun, caught during the Aether Paradise story.
Pheromosa (570, Gen 7). Impossible-legged cockroach. Ultra Beast in Moon / Ultra Moon.
Volcarona (550, Gen 5). Fire/Bug moth. Catch a Larvesta egg from an NPC on Route 18 in Black/White and grind it to level 59.
Scizor (500, Gen 2). Steel/Bug, still popular. Trade a Scyther holding a Metal Coat, or use one via item swap in Legends: Arceus.
Rock
Tyranitar (600, Gen 2). Rock/Dark pseudo. Evolve Pupitar at level 55 in Gold/Silver, Larvitar is a Mt. Silver find.
Diancie (600, Gen 6). Rock/Fairy jewel. Event-only mythical for Omega Ruby / Alpha Sapphire.
Terrakion (580, Gen 5). Second musketeer, Rock/Fighting. Victory Road catch in Black/White.
Stakataka (570, Gen 7). Rock/Steel building. Ultra Beast in Ultra Moon.
Rhyperior (535, Gen 4). Rhydon with rockets in its palms. Trade a Rhydon holding a Protector.
Ghost
Giratina (680, Gen 4). Distortion World host, Origin form is 680 too. Catch at Turnback Cave in Diamond/Pearl, or the Distortion World in Platinum.
Marshadow (600, Gen 7). Ghost/Fighting mythical. Event-only for Sun/Moon in 2017.
Dragapult (600, Gen 8). Ghost/Dragon pseudo. Evolve Drakloak at level 60 in Sword/Shield.
Blacephalon (570, Gen 7). Clown bomb. Ultra Beast in Ultra Sun.
Gholdengo (550, Gen 9). Coin gremlin. Evolve Gimmighoul once you gather 999 Gimmighoul Coins in Scarlet/Violet.
Dragon
Rayquaza, Dialga, Palkia, Reshiram, Zekrom. All 680. Every box legendary from Gens 3 through 5 tied for the same budget on this list.
Rayquaza (Gen 3) at Sky Pillar in Ruby/Sapphire. Dialga (Gen 4) at Spear Pillar in Diamond and Platinum. Palkia (Gen 4) at Spear Pillar in Pearl and Platinum.
Reshiram (Gen 5) at N's Castle in Black, Dragonspiral Tower in White 2. Zekrom (Gen 5) at N's Castle in White, Dragonspiral Tower in Black 2.
The next-highest pure or partial Dragons drop to Kyurem 660 and Kingdra / Salamence / Garchomp / Dragonite / Hydreigon / Goodra / Dragapult / Baxcalibur at 600, all obtainable through normal evolution lines in their debut regions.
Dark
Yveltal (680, Gen 6). Same as above, Dark/Flying. Y story catch.
Tyranitar (600, Gen 2). Dark/Rock. Same evolution path.
Hydreigon (600, Gen 5). Dark/Dragon hydra. Evolve Zweilous at level 64 in Black/White.
Roaring Moon (590, Gen 9). Paradox Salamence. Catch in Area Zero at the end of Scarlet.
Chi-Yu (570, Gen 9). Dark/Fire goldfish. Catch at the Firescourge Shrine in Paldea after clearing the yellow stakes.
Steel
Zacian Crowned Sword (720, Gen 8). Steel/Fairy when holding the Rusted Sword. Story catch in Sword.
Zamazenta Crowned Shield (720, Gen 8). Steel/Fighting, same setup in Shield.
Dialga (680, Gen 4). Steel/Dragon time god. Spear Pillar in Diamond and Platinum.
Metagross (600, Gen 3). Steel/Psychic. Evolve Metang at level 45 in Hoenn.
Magearna (600, Gen 7). Clockwork mythical. Distributed via QR code with the Volcanion movie in 2016, playable in Sun/Moon.
Fairy
Xerneas (680, Gen 6). Life deer. Catch at Team Flare Secret HQ in X.
Zacian Hero of Many Battles (670, Gen 8). Pure Fairy without the sword. That is the pre-form-change version you fight in the story.
Diancie (600, Gen 6). Rock/Fairy again, event mythical.
Enamorus (580, Gen 8). Fairy/Flying Kami added in Legends: Arceus. Catch in the Scarlet Bog after finishing the Hisui Pokédex postgame.
Tapu Lele (570, Gen 7). Psychic/Fairy guardian of Akala. Catch at the Ruins of Life on Akala Island in Sun/Moon.
A few honest caveats
Where a Pokémon shows up on more than one list I left the strongest instance in each. Ho-Oh is on both Fire and Flying because both are legitimately its highest-BST option for that type.
I stuck to base forms across the board. Mega Rayquaza at 780 would win basically every list it touches, and Ultra Necrozma would flatten Psychic. The lists get boring fast if you allow one-off transformation stats.
If you want to test your BST intuition without memorising all of this, the fastest way is repetition. Play a few Higher or Lower rounds in the Daily Challenge or Unlimited, and the numbers start to stick faster than a spreadsheet ever would.