So this is kind of controversial because Pineco sucks shit. Like, it's total dogass. Unusably so. But. Turns out Forretress is pretty damn good!
If you grind Pineco (or are smart and use the day care) you end up with a dude who hits decently hard, outspeeds a surprising amount of stuff, and hard walls about 55% of the game. Bug Bite gives you decent stab options and your usual Normal/Dark (Strength/Payback) let's you hit stuff neutrallly. Sorry will usually 2/3hko stuff but opponent's will usually 6-7hko when they deign to attack so you're Gucci there.
Sorry has good matchups against Pryce and Claire, and absolutely trashes Rival especially if you choose meganium. It also wrecks team rocket which is especially useful when you need to tank explosions from various weezing/electrode. Great matchup vs Koga, good matchup vs Will and Karen, and can contribute vs Lance
FORRY is good Mon, much better than I'd have ever guessed
Just basing this on the OP, so sry if any of these have been nominated already. Also sorry for not following the format; I just noticed it after typing like 90% of my post and fuck going back to edit it at this time of night. I'm basing these on my ongoing honourable (but otherwise unrestricted) run:
Nominating Machop (Machamp) for A and Machop (Machoke) for B rank
Obtained very early with next to no effort required (trade for the most common Pokemon on the adjacent route
Not sinfully low level when first obtainable (trades at same level as the Drowzee you send, unlike Heracross which is caught at a measly level 2-5)
Solos Whitney with Karate Chop/Low Kick and Pryce with Revenge while also having a spectacular matchup vs. Jasmine with Revenge or Submission and matching up well vs a number of unavoidable battles, including v.s. Sudowoodo and v.s. the two beauties just outside Ecruteak City.
Evolves at a reasonable level early (access to Machoke from around the time you'll be getting your fifth badge unless you're playing under-levelled) and can instantly be evolved a second time with no drawbacks wrt level-up movepool.
Access to a lot of valuable HM moves, namely Strength and Rock Smash, and as such reduces need to rely on HM slaves (granted I'd usually put Rock Smash on smth like Geodude instead which benefits more from the stat dropping utility than it does from the ability to hit hard with 4 differently-typed attacks)
Access to moves which are very good for the vast majority of the pre-Kanto run from a very early point in the game, namely Strength, Payback, and Rock Tomb.
Nominating Geodude (Golem) for A rank and Geodude (Graveler) for B rank:
Bones Falkner, Bugsy, and Whitney; super good matchup vs Jasmine too provided you have something in the back that can deal with Steelix 'cuz even with SE damage EQ is doing fuck all to that monster.
Obtainable before the first trainer battle in the game
Solos most youngsters, which in turn is useful for preserving teammates' PP in honourable runs (honourable turns the game into an endurance test rather than a difficult game tbh)
Solos most of Team Rocket as well as having a solid matchup vs. a big chunk of the trainers in the Olivine Lighthouse.
Learns Earthquake at level 29 if you delay evolution.
Access to Rock Smash while being one of the Pokemon which can actually make use of it until sometime in the mid-late 20s, and even then it's not like it even really needs four moveslots 'cuz [rock move] or Earthquake is what gets clicked 99% of the time anyway; means you don't need to lug around dead weight in the form of a HM slave.
Access to Rock Polish early on, which is nice for alleviating certain matchups where you need to be able to move before things like the omnipresent Hypnosis or dumb Team Rocket's Zubats' fucking Supersonic bullshit, although it will ultimately probably replace it at some point around the time you learn Earthquake unless you don't have Dig on it for whatever reason.
Nominating Gastly (Gengar) for S rank and Gastly (Haunter) for A rank:
Obtained before Falkner, meaning that the game is at a low enough level for its shitty level 4 encounter to be forgivable
Solos Sprout Tower, rival (exc. starter unless you've obtained the Sludge Bomb TM+picked Totodile), Whitney, Chuck and a fuckload of other trainers thanks to its typing and access to Curse; seriously, Ghost+Curse is fucking great to have vs so many trainers in this game.
Learns Night Shade reasonably early, meaning that you don't need to rely on Lick for too long, and can learn Shadow Ball from Morty's TM from as early as level 20 if you opt to solo his gym with Girafarig, although more likely you will be at level 25 by that point and as such have the choice between using the TM there and then or saving it for a teammate and relying on Shadow Punch, which is still really good for the most part until lv 33 when it learns SBall via level up.
Can be evolved into Gengar at level 25 (the level you will probably be before entering Morty's gym assuming you play the most EXP-efficient grindless route through the game* with 0 learnset-based drawbacks (all level up moves are identical and learned at the same level), which in turn means that you can solo Morty's gym with just Gengar if you really want to (fight Morty at level 26 or 27 and you beat his Gengar with very few issues; rest of gym stands 0 chance as it's all outrun+OHKOed)
Insane movepool thanks to insane early-game TM access (Thunder, Thunderbolt and Shadow Ball all available before the game becomes nonlinear, and access to Sludge Bomb before you even need to fight a fifth gym leader)
*all of Violet-entrance Dark Cave, Mt. Mortar ground floor and Burned Tower fully explored and all routes/dungeons up to and including Lake of Rage and Olivine Lighthouse completely cleared of trainers before fighting Morty.
Nominating Abra (Alakazam) for A and Abra (Kadabra) for B
Obtained very early and very easily thanks to the free Fast Ball you get from Kirt after beating Team Rocket in Slowpoke Well (just take put a pre-Azalea Ratatta at the front of your party and run around in grass until you spot one then throw the Fast Ball; it's aesthetically appropriate too!)
Almost solos rival and Team Rocket; solos Chuck; generally threatening enough to put in a lot of work in the vast majority of neutral matchups too + suuuper good vs. Morty, albeit not quite a solo unless you get a level 15 Alakazam or something.
Level 15 Alakazam with no movepool/learn-level drawbacks over Kadabra
Insane TM learnset, with access to Thunder, Thunderbolt, Shadow Ball and Focus Blast all before the game becomes nonlinear.
Learns Flash and only really needs 1 of its moveslots (although giving it Shadow Ball in one of the three flexible slots is usually a good choice), making it very useful when it comes to dealing with both Dark Cave and Whirl Islands (as well as Rock Tunnel and Cerulean Cave if we're talking about Kanto areas too).
Also this is a much more minor thing, but Teleport is a really convenient tool in general before Fly becomes available when exploring routes which require going through large areas of grass to traverse (makes getting back to Ecruteak City from Lake of Rage or any of the remote caves a total non-issue, which is incredibly useful as that will generally be a central hub in the period of exploration before fighting Morty, or indeed before tackling any of the three nonlinear gyms (as you should go to Union Cave immediately after obtaining the ability to Surf) as you don't need to use any Pokemon centres before reaching caves. You shouldn't need to use a Pokemon center to get to any of them and it saves you having to waste Repels travelling through the "forward"-movement only patches of mandatory grass (i.e. most of them). Dig user+Abra line is a generally good backbone when it comes to overworld exploration throughout the majority of the Jhoto half of the game.