>>45712813Analysing in-game scenarios...
Most of psychic Pokemon since STAB is all they need. Drowzee, Kadabra, Slowpoke (who also gets Surf via HM), Mr. Mime and Jynx (although she gets Ice Punch instead of psychic STAB). The only exceptions are Staryu and Exeggcute since they get no good moves via level up.
Diglett is insanely good since it starts with 100 BP STAB and gets Slash later (which crits all the time so it does similar damage to Dig). These two attacks hit everything not named Aerodactyl for neutral/SE damage.
Doduo is relatively good because it has access to Drill Peck before evolving and Tri Attack after evolving. Normal + Flying combo covers everything bar rock types.
Snorlax starts with Headbutt, Amnesia and Rest so it hits relatively hard and it's not easy to kill. Few levels later it gets Body Slam and that move is honestly enough for everything that's not Gastly or Graveler.
Machop doesn't have that great learnset on paper but it's good when you consider everything else. Karate Chop has a massive change to crit (~70% on Machoke and ~86% on Machamp) so it's power is more similar to Double-Edge. Early on, Machop also gets Low Kick which isn't great but it's a STAB coming from huge base Attack stat. Karate Chop+Low Kick cover everything bar Gastly.
Mankey is the same in Yellow but its Karate Chop is guaranteed to crit. It's attack stat is lower than Machamp's.
Zapdos starts with Drill Peck and gets Thunder after one level up. These two cover the whole game and they deal HUGE damage.
That's mostly it. I would say that Zapdos and Diglett are the best (if we ignore psychic types).