The Mage Slayer (Bard/Fighter/Rogue)
Some players just hate Wizards. You don't know what it is about Wizards that you hate, but boy do you hate them. Probably those pointy hats or their scrawny arms. Whatever the reason, when it comes to massacring mages at all levels of the game, accept nothing less than the Mage Slayer grappler. This is an extremely narrow build that, although useful against a variety of enemy types and classes, is at its best against those pesky magic users. There are tons of ways to build an antimage grappler (Wizard with Antimagic Field is another route), but this build will be the most relevant at all levels of the game, and is most likely to give your DMs magic practitioners a serious head/neck/throat ache.
 
The build functions around the almighty Silence spell, a no-save-allowed way to stop most magic cold. Your main class is College of Lore Bard, which gets you access to an arsenal of mage-murdering spells and gives you the highest possible single grapple checks of any class. It is critical to have high single grapple checks as a Mage Slayer because that initial grapple in the area of Silence is the most important. Once they are stuck there, they just can't do anything. Setting up that Silence will require a few different combinations of features, actions, and spells. As wizards scale up their power, your combos will scale with them. But because each engagement is so resource intensive, the build is heavily dependent on rests in between engagements, That play style might not suit everyone, but for those who want to give mages (and your DM) nightmares, this is the build for you.
 
As a final note, I emphasize this again: the build really is a single target, mage killing optimization. It's narrow, it's a nightmare for wizards, and it's a bit...strange, as far as grapplers go...
 
Starting Race: Human
Although you can go Mountain Dwarf in this build, Human is a better option because of how feat intensive the build is, especially at early levels.
 
Ability Scores: Here's your 27 point buy array assuming shameless optimization choices.
Str: 15 (Human +1 - Show those wimpy Wizards how it's done)
Dex 13 (Required for the Rogue multiclass)
Con 10 (This is a single-target, glass-cannon build. We can't afford to max out HP at the expense of other stas)
Int 8 (Int saves just aren't all that common, and those you do have to worry about shouldn't even work in an area of Silence)
Wis 10 (Never dump this; Wisdom saves tend to govern fear, and you do not want to be frightened as a grappler)
Cha 15 (Human +1 - More Charisma means more Cutting Words attempts)
 
Fighter 1
Human level 1 feat: Tavern Brawler
As with many grappling builds, start in Fighter to get the Heavy Armor Proficiency without spending a Feat. We get Warcaster both to concentrate on our spells in the fight, and to cast spells while wielding. We are also going to get the Dueling fighting style, and Tavern Brawler so we can grapple after making an attack (we will need that attack eventually to cause damage to trigger Mage Slayer).
Fighter 1 / Bard 1
With Heavy Armor acquired, we go straight for our Bard features/spells at level 3.
Fighter 1 / Bard 2
Fighter 1 / Bard 3
Expertise? Check. Cutting Words? Check. Silence? Check. Enhance Ability? Check. You now have access to your most basic combo. Cast Enhance Ability on yourself before the fight. At the beginning of the fight, walk over to the target and grapple them with advantage. Next turn, cast Silence on the area. We will defnitely do better than that later, but it's only level 4.
Fighter 1 / Bard 4
Level 4 Feat: Mage Slayer
Here's our next piece of the combo. Starting at level 5, you will encounter more situations where enemies have preexisting concentration-based spells before you grapple them. Those often need to go away if you are to win the fight, and Mage Slayer is going to get that done.
Fighter 1 / Bard 4 / Rogue 1
To break concentration, we need big damage rolls on a single attack at the start of the fight. Rogue is going to get that done. Level 1 gets you Sneak Attack; you already have Expertise from Bard..
Fighter 1 / Bard 4 / Rogue 2
Cunning Action normally rocks at this level, but you generally won't use it because of Tavern Brawler. We are really going into Rogue to get the next class feature.
Fighter 1 / Bard 4 / Rogue 3
Assassinate plus Mage Slayer plus surprise equals impossible concentration saves. Now that we have finished out the Mage Slayer feature tree, we can change our combo to really ruin a mage's day. For your pre-fight buff, you have two options from the Bard 2 spell list. You can either stick with Enhance Ability and use Stealth to approach a target, or you can use Invisibility. Either way, you just want to make sure your target is surprised. Walk up to them and stab them with your improvised weapon short sword; it shouldn't take too much DM convincing to improvise a short sword. The attack will automatically score a critical hit for 6d6+5 damage (2d6 short sword, 4d6 sneak attack, 3 strength, 2 dueling). That assumes no magical buffs that add damage die, and you are already at an expected DC 13 Concentration save that they must make with disadvantage. Then grapple them and hold them in place until next turn when you can Silence.
Fighter 2 / Bard 4 / Rogue 3
Action Surge. What an imbalanced ability. Now you can do the same combo as above but ALSO cast Silence in the same turn you stab and grapple.
Fighter 3 / Bard 4 / Rogue 3
Getting to Fighter 3 gets you Battle Master, which will almost always be a Trip Attack applied to your opening stab. It's also an added 2d8 damage (1d8 doubled) on your automatic critical hit, which ups that Con save to DC 17 with disadvantage on the roll. Now your combo looks like this: Sneak up and stab to force a concentration save. As part of that sneak, apply a trip attack to get them prone. Then take a bonus action to grapple off Tavern Brawler. Now Action Surge, drop your improvised Short Sword, and cast Silence.
Fighter 4 / Bard 4 / Rogue 3
Level 4 Feat: Warcaster, Lucky, Magic Initiate
Bunch of different feat options here. Go Warcaster to guarantee that Silence doesn't get cracked. Go Lucky for an added guarantee on the initial grapple check. Or go Magic Initiate to gain Find Familiar, which you can use to take the Help action on that initial grapple (freeing up your pre-battle spell for Invisibility).
Fighter 5 / Bard 4 / Rogue 3
Extra Attack is the next evolution of your mage-murdering combo. Now that you have two attacks, you can replace one with a shove attempt, and modify the opening stab with Menacing Attack instead of Trip Attack. Stalk up to your target and take the attack action. Apply Menacing Attack to the stab and force a DC 17 (average) save with dsiadvantage. If they fail the wisdom save on the Menacing Attack, now they have disadvantage for the rest of the turn. Use shove in place of your second extra attack, and grapple with Tavern Brawler as a bonus action. Drop the sword, action surge, cast Silence, and watch your DM and his wizard cry.
Fighter 5 / Bard 5 / Rogue 3
Fighter 5 / Bard 6 / Rogue 3
The big bonus here is Magical Secrets through College of Lore. And boy, there are a lot of options to pick from, so this is a great way to round out your skillset. Two standout options I want to discuss are Blinding Smite and Counterspell. Counterspell is a somatic-only spell that will work even with Silence, and it's the best way to guarantee that your caster is totally locked down. Blinding Smite is a Paladin spell that requires concentration (so no invisibility), but adds 3d8 damage to your attack roll and forces a save to avoid blindness. If you connect with Assassinate on that opening hit and auto crit, your save will be basically impossible to match: an AVERAGE save of DC 31 made with disadvantage. Even if you don't automatically crit, it's still a DC 17 average save with disadvantage. Those are just two options you can take at this level.
From Level 14 onward, I recommend that you continue progressing in Bard to get that level 10 Magical Secrets feature. Then you can paly with those last two levels wherever you want.
 
One key to this build is beating the scariest spell of them all: Freedom of Movement. It's actually not that hard, but it just requires a combo modification. You will still open with your massive damage spike, still grapple the target with Tavern Brawler, and still shove them with your attack. But instead of casting Silence, you will cast Dispel Magic and try to strip the buff away. The DC is 14, and your bonus will be 3 + 1/2 of your proficency bonus (thanks Jack of all Trades). If you have the presence of mind to Enhance Ability (Charisma) yourself beforehand, you will have advantage on that check. After you remove it, just have a Counterspell ready for the intervening turn to stop anything your opponent tries. Then just Silence at the beginning of your second round.
 
That description should give you some idea of how narrow this build is, but also how powerful it is at shutting down a single spellcasting target. Despite this narrowness, there are lots of ways to increase your flexibility; Bards have so many useful spells in that regard, and you definitely aren't a shabby grappler even your target isn't a Mage. Just figure out ways to adapt your combo and you will be ready for grappling anyone, whether scrawny-armed and pointed-hatted or not.