Pathfinder 2e Character Discussion

A Warhammer+Freehand setup is a pretty good baseline. Prone + Grabbed is a nasty debuff combo, and you can inflict the first condition with Hammer crit spec, and the second from Combat Grab from lv 2 Fighter. Beyond that, you're kind of free to explore any build paths however you please.

You could grab a spiked gauntlet and pairing rings to make Combat grabs more accurate.

You could invest into some handwraps of mighty blows and go hard into wrestler for the special moves that require unarmed strikes.

You could dip into some spellcasting archetypes for Enlarge so that you can grapple huge creatures.

I'm playing an Animal Instinct (Snake in my case, Deer is probably better) Barbarian with Wrestler (Free Archetype but honestly if PFS you can just archetype into Wrestler as normal) for my grappler. It works pretty well, but yeah Monk is probably better if you really want to focus on maneuvers like grappling. Barbarian will get you higher damage than an unarmed Fighter will while Monk I think gets you more defenses and maneuverability (I could be wrong, never actually played a monk).

Honestly, Monk + Wrestler or Monk + Barbarian (giant) would probably make a better grappler overall, and do more damage over time, since the Monk inherently does more damage from unarmed attacks. I know what you mean about the fighter doing better damage, but that's sort of predicated on playing a fighter as a plain vanilla fighter. Once you've sort of focused on grappler, you're chucking part of the fighter's advantages out the window.

If you do want to stay with fighter as your main class, my opinion is that wrestler is clearly the better choice, mostly because it's entirely focused on grappling. Take farmhand background, snagging strike as 1st level class feat, wrestler dedication at 2nd which gives you titan wrestler, then combat grab at 4th. If you make it all the way to 8th, that's when the really fun feats come online, like whirling throw.