They really aren’t messy. You can use one of your attacks to initiate a grapple, which is a simple contest of the attacker’s Strength (Athletics) vs the defender’s choice of their Strength (Athletics) or their Dexterity (Acrobatics). If the attacker wins, the defender’s speed becomes 0, and can’t be increased above 0. Their speed goes back to normal if the attacker becomes incapacitated, the defender is moved out of the attacker’s reach, or the defender uses an action to escape the grapple with another Strength (Athletics) or Dexterity (Acrobatics) vs Strength (Athletics) contest.
That’s literally all there is to it, some pretty simple rules for how to establish and escape the grapple, and the effect that a grappled creature can’t move. I struggle to imagine grapple rules less messy than that.