Human(variant) with Sentinel or Martial Adept Feat; Battle Master
One of the challenges with your builds multiple goals is the use of taunting as a mechanical means of influencing your enemies. You can't get that until level 3 with a Fighter unless you take the Martial Adept feat at level 1. (Variant Human Option, PHB). You also can't "tank" if you don't prioritize for AC. You can do a few things that will make enemies focus on you, and that allow you to lock down or attempt to control your enemies. If you want to tank, you are playing a controller style more than a damage taking/reducing role due to your dex based, no shield, approach.
You can talk trash to them at any time, since talking during your turn does not harm your action economy.
Level 1: Sentinal Feat + Defense Fighting Style.
Your Dex should be 16, your Constitution 16. (there go your two +1's for vHuman).
Work your other stats to taste. You need all of the HP that you can get given your goals.
OR
Level 1 (short term gain, long term cost): Martial Adept feat + Defense Fighting Style
Your battlefield control from Sentinel is traded off for the trash talking control abilities using the Martial Adept feat and selecting Goading attack (and one other) right of the bat. Something like Parry or Menacing Attack (frightened enemies, that's a good thing) might fit your theme pretty well.
- You learn two maneuvers of your choice from among those available to the Battle Master archetype in the fighter class. (PHB, ch 6).
A constraint of this approach is that for these two maneuvers, your supremacy dice remain d6, whereas for all others they go up as your level in Battle Master go up.
- @Falconer suggeted the Defensive duelist feat at level 1, which has some advantages in the early going. It also adheres to your theme of using your rapier to make you "more tanky." Your reaction is used to add +2 to your AC(for one attack during your turn), but it does not offer the controlling / taunting feautres that Sentinel or Martial Adept would offer. If you are willing to wait to level three to get taunty stuff via battle master, defensive duelist makes your defense (for one attack) stronger per turn at no cost in resources, but once you get reaction based resources as Battle Master, now your benefits may trip over each other. You need to decide what's more important during the early going, controlling, taunting, or a bit more AC early on. You have to make a choice; can't have it all coming out of the gate. It's a case of 'pay me now or pay me later' (At level 5, the AC bonus is +3; at 9, +4; at 13, +5)
Defense fighting style. +1 AC.
With Studded leather, Defense Fighting Style, and +3 for Dex, your AC is 16, and will be for a while. Based on your constraints, that's the best you can do.
Optional: Straying slightly from your desired look, you can pick up a breastplate when you can afford it; your AC will be 17. You can wear your a tabard over it; check out Renaissance paintings, loads of rapier wielding and breastplate wearing dandies. See also the PHB illustration of a Noble: wears a breastplate. Or, to stay thematic, stick with the studded leather. Your choice. At level 4 with your first ASI into dexterity, studded leather + dex and breastplate are a wash. At level 6 with a Dex of 20, Studded Leather + dex is AC 18.
Lock Down part 1
SENTINEL feat
- When you hit a creature with an opportunity attack, the creature’s speed becomes 0 for the rest of the turn.
- Creatures provoke opportunity attacks from you even if they take the Disengage action before leaving your reach.
- When a creature within 5 feet of you makes an attack against a target other than you (and that target doesn’t have this feat), you can use your reaction to make a melee weapon attack against the attacking creature. (PHB, Feats, Chapter 6).
Item 1 stops a creature from moving, item 2 makes them pay a penalty for moving away from you, item 3 makes them pay a penalty for attacking someone other than you. And you can talk trash the whole time.
Lock Down, part 2: choose Battlemaster at level 3.
As the other answers note, here is where your trash talking has mechanical back up. I'd agree with T.J.L's suggestion of Cavalier, but the features come on-line a bit late. If you are willing to wait, then Cavalier has some nice class features; Battle Master Maneuvers are limited per short rest/long rest regeneration.
Goading Attack: Get the enemy's focus on you
Parry: Reduce damage opportunities for enemies.
Maneuvering Attack: Get your allies out of the way.
The synergy with Sentinel with a lot of these maneuvers gives your Fighter the feel of a Controller.
Other maneuvers can be chosen to either protect you allies, boost AC or make your opponents ability to maneuver difficult, but those three would be your bread and butter.
ASI:
At level 4, boost your Dex to 18.
At level 6, Boost your Dex to 20.
At level 8 ASI or Feat to taste. (Consider Alert, see below)
At level 10 Dueling Fighting Style. (Thematic)
At level 12 ASI or Feat to taste. (At this point, you are approaching the end of this published adventure.
For more tankiness: consider Defensive Duelist Feat at level 6 or 8.
This feat may compete with your Maneuvers for using your reaction spot - which makes it a tricky choice - but adding your proficiency to your AC as a reaction can increase your front line tankiness. Going from 16 to 19 AC can save some damage from ever happening. At level 9 that AC bonus goes up to 4. The problem with this feat is that if you are subject to multiple attacks in a round, it only works against one attack. As you go higher in level, a lot of enemies have multi attack, or mooks who try to swarm you.
Why the Alert feat helps this concept in mid to late game
Under the idea that 'the best defense is a good offense', and your stated goals ...
- You add 5 to your initiative score. You already have a nice
initiative score with your 20 Dexterity. You going first more often
helps you set the table for a melee combat. You want to be in the enemy's face early and often.
- Your PC can't be surprised. This, tied to your higher initiative,
gives you more opportunities to 'get in the face' of your enemies
early in the fight.
- Enemies who are hidden or invisible do not get advantage when
attacking you.
This is an inverse tankiness deal: advantage on attacks against you (who are trying to draw attacks) from hidden or invisible creatures is a practical 3-5 increase in the attack roll against you, or a net reduction of your AC of 3-5 for that attack. Preventing that helps you be "tanky" somewhat.
For one of your ASIs, you may want to boost your Wisdom Score, or better yet get Resilient / Wisdom (proficiency bonus added to your wisdom save is a great idea) as you get deeper into the plane and the fear / other Wisdom save powers of your enemies put your freedom of action at risk. Fiends have a variety of powers that put your Wisdom saves to the test.
Your character's build goals are, quite frankly, in conflict with optimization for either damage or tankiness, but they do look to be optimized for fun.
Lay on, MacDuff!
Suggested path to achieve your goal:
27 Point Buy. S 12 D 15 C 15 I 8 W 11 Ch 10 ... vHuman ... (2 +1s)
Background: Sailor (Swashbuckler Theme)
Skills: (Br) Athletics, Perception; (F) Intimidation; Animal Handling; (Feat): Acrobatics (Swashbuckler theme)
At level 1; S 12 D 16 C 16 I 8 W 11 Ch 10
Feat Sentinel
At Level 3; Battle Master (See Maneuvers above)
At level 4: S 12 D 18 C 16 I 8 W 11 Ch 10
At Level 6: S 12 D 20 C 16 I 8 W 11 Ch 10
Most of your build is done at this point, since Battle Master maneuvers are where you get taunt / control powers.
At Level 8: S 12 D 20 C 16 I 8 W 11 Ch 10
Feat Alert. (Or Wisdom, Resilient) You will have learned some things during play with your group that will inform your feat selection here; boosing Wisdom saves may be the better idea if your support casters can't buff your Wisdom saves)
At Level 10: Duelling Fighting Style (Thematic)
At Level 12: S 12 D 20 C 16 I 8 W 12 Ch 10
Resilient, Wisdom, Feat (Or Alert at this point if Res Wis was taken at 8)
While Tough is an appealing feat to make you more tanky, IMO Alert will help you get hit less often.
What do I do with my other hand?
Hold a torch or a bullseye lantern, or a thing that your cleric cast the Light Cantrip on. You don't have darkvision.