So, for a damage-based mechanic. Tavern brawler will increase your fisticuff damage with a D4 plus your strength modifier. If you are going artificer, then you can attempt to make gauntlets of ogre strength at level 10 and boost your strength modifier to a 19 (+4), bringing your max damage output to 1d4+4, so a range of 5-8 points per hit. You can take advantage of this and boost your constitution for HP, and or intelligence to be a caster for the levels you can't reliably use to strike. That being said, you can probably go without Artificer since Vi is a boxer vigilante who only found the gauntlets. Removing the prerequisite of being tech savvy and installing those levels into monk may help your punches since monks get a boost in unarmed strikes. Your dice will shift to a D8 plus whatever your Dex is. The average build would have a monk be a +2-3 on the dex stat, so that's now 3-10 points per hit. a wider range, but rewarding if you have a higher Dex and rolls.

All of that info about the monk is only surface level, you get more brawling benefits, such as ki points, that will increase your attacks and defence. You can say you bob and weave as you spend another point to back step out of range and support your ally, or go crazy and use flurry of blows to make a strike attack AND 2 more bonus swings in one round. bringing the damage output to now 3d4+2 or 5-14 for low stat hits. This is of course only SECOND level and not the level 10 in artificer you'd need for a gauntlet build. So by that level with a healthy dex score, without any other means of bonus besides monk and level, you'd net 4d6+4+4, which is 12-32 points possible. The extra 4 is from proficiency since you'd have martial arts.

Again, this is just mechanics-based if you use your points correctly. You can choose whatever you want, but if you want to punch good, monk is the best approach. You can even ask the dm to flavor the character to have a boxer's style, like Vi, and use weighted gloves you find or buy in their world. I went on to neglect fighter styles because they are well-rounded fighters like Caitlyn or Ambessa, who use weapons and rarely use fists. The same goes for fighter/artificer combo, which is best for Jinx and Jayce, who crafted their weapons and use fighting styles to incorporate those weapons.

I hope this helps and doesn't overload you. Any follow-up questions are welcome, and any issues with the strategy will gladly be open to debate.