The highest catch rate possible is 255. In Pokedex order, they go:
Caterpie, Weedle, Pidgey, Rattata, Spearow, Ekans, Partner Pikachu, Sandshrew, Zubat, Oddish, Diglett, Meowth, Poliwag, Bellsprout, Geodude, Magikarp, Partner Eevee, Sentret, Hoothoot, Ledyba, Spinarak, Hoppip, Wooper, Poochyena, Zigzagoon, Wurmple, Lotad, Seedot, Shroomish, Slakoth, Nincada, Nosepass, Skitty, Numel, Spoink, Spinda, Trapinch, Swablu, Baltoy, Feebas, Spheal, Clamperl, Starly, Bidoof, Kricketot, Budew, Bronzor, Bonsly, Patrat, Watchog, Lillipup, Purrloin, Pidove, Roggenrola, Audino, Tympole, Sewaddle, Venipede, Maractus, Minccino, Vanillite, Ferroseed, Elgyem, Bunnelby, Fletchling, Scatterbug, Pikipek, Yungoos, Grubbin, Necrozma, Skwovet, Rookidee, Blipbug, Nickit, Wooloo, Chewtle, Yamper, Rolycoly, Applin, Silicobra, Arrokuda, Imipdimp, Eternatus, Lechonk, Tarountula, Smoliv, Nacli, Wiglett, Terapagos
The lowest catch rate possible is 3. In Pokedex order, they go:
Articuno, Zapdos, Moltres, Mewtwo, Raikou, Entei, Suicune, Lugia, Ho-Oh, Beldum, Metang, Metagross, Regirock, Regice, Registeel, Latias, Latios, Kyogre, Groudon, Jirachi, Deoxys, Uxie, Mesprit, Azelf, Dialga, Palkia, Heatran, Regigigas, Giratina, Cresselia, Manaphy, Darkrai, Arceus, Victini, Cobalion, Terrakion, Virizion, Tornadus, Thundurus, Reshiram, Zekrom, Landorus, Kyurem, Keldeo, Meloetta, Genesect, Zygarde, Diancie, Hoopa, Volcanion, Type: Null, Silvally, Tapu Koko, Tapu Lele, Tapu Bulu, Tapu Fini, Magearna, Marshadow, Zeraora, Meltan, Melmetal, Kubfu, Urshifu, Zarude, Regieleki, Regidrago, Glastrier, Spectrier, Calyrex, Enamorus, Koraidon, Miraidon, Okidogi, Munkidori, Fezandipiti, Pecharunt
Random trivia:
- The Beldum line are the only non-legendaries with a catch rate of 3.
- Watchog is the only evolved Pokémon with a catch rate of 255.
- Necrozma and Eternatus have the highest catch rates of any legendary.
Source
Hope I helped!
