Unarmed Fighter/Rune Knight is, imo, Best in Class.
I still suggest you dip into Rogue for 2 levels for the peerless mobility of bonus-action Dodge, but otherwise, it's all you need.
The only critical Rune is available immediately, Frost Rune. Frost Rune gives you an entirely unique, untyped bonus of +2 to Athletics:
You can invoke the rune as a bonus action to increase your sturdiness. For 10 minutes, you gain a +2 bonus to all ability checks and saving throws that use STR or CON. Once you invoke this rune, you can’t do so again until you finish a short or long rest.
You also gain Giant's Might, which is revolutionary, and handles our Strength Advantage needs, and also Enlarges us without sacrificing action economy much. One bonus action and you've got Advantage on athletics, and now are super-sized (initially Large, eventually Huge) and do free damage when slamming your enemy (initially d6, eventually d10).
When you become Huge, you also gain +5 reach. This means you have a Reach of 10, and can Grapple a Gargantuan character, and have no movement speed reduction (unless encumberance) when hauling Medium characters around.
(As a subtle perk, this doesn't contradict getting Enlarge cast on you, so you could actually become Gargantuan, which lets you haul around Large characters, and ... if you're using it, you can grapple Colossal size creatures now.)
As a bonus action, you magically gain the following benefits, which last for 1 minute:
- If you are smaller than Large (/ Huge), you become Large (/ Huge), along with anything you are wearing. If you lack the room to become Large (/ Huge), your size doesn’t change.
- You have advantage on Strength checks and Strength saving throws.
- Once on each of your turns, one of your attacks with a weapon or an unarmed strike can deal an extra (1d6/1d8/1d10) damage to a target on a hit.
You can use this feature (proficiency) times, and you regain all expended uses of it when you finish a long rest.
Bonus fun stuff:
1: the Fire Rune gives you the ability to gain essentially a "third grapple" by restraining:
In addition, when you hit a creature with an attack using a weapon, you can invoke the rune to summon fiery shackles: the target takes an extra 2d6 fire damage, and it must succeed on a STR saving throw (DC:18) or be restrained for 1 minute. While restrained by the shackles, the target takes 2d6 fire damage at the start of each of its turns. The target can repeat the saving throw at the end of each of its turns, banishing the shackles on a success. Once you invoke this rune, you can’t do so again until you finish a short or long rest.
2: the Cloud Rune gives you the ability to redirect the enemy's attack against you to anyone else, even the other grapplee if double grappling (which is the most fun visual for me)
Once per short rest, when you or a creature you can see within 30 ft. of you is hit by an attack roll, you can use your reaction to choose a different creature, other than the attacker, within 30 ft of you to become the target of the attack instead, using the same roll.
TL;DR: All the things you need to Grapple, every "must have" for cross-classing, is handled by Rune Knight. Rogue is still a super-valuable dip just to hurl people off cliffs, obviously, but is no longer mandatory - I don't even know when I'd consider stopping escalating Fighter to look at Rogue, since I can just take the Skill Expert feat now to gain Expertise if I want it. In a perfect level 20 scenario, you want 18 Fighter/2 Rogue, but I genuinely think you probably just go up the Fighter tree and don't look back.
That said, if Disarm is not available per the DMG, a strong argument can be made for how wonderful Battle Master is, and I respect that. Also, flavor-wise, Battle Master will never not be good. But pure optimization, I cannot perceive a better path than a Rune Knight Goliath grappler.