You want to choose a Khajiit at the beginning of your game. As you may know Khajiit's have extra Unarmed damage because of their claws. Your claws deal 15 points of damage! If you didn't know the base damage of an Daedric Sword is 14. So you actually start with one of strongest weapons (in terms of base damage) in the entire game.

You will need the following perks to get the most damage out of your fists.

Heavy Armor
Juggernaut 5/5 - Increases armor rating for Heavy Armor by 100%.
Fists of Steel - Unarmed attacks with Heavy Armor gauntlets do their armor rating in extra damage. (Upgrading your gauntlets will not increase their damage! base armor rating = extra damage)
The other Heavy Armor perks are optional but highly recommended.

Enchanting
Enchanter - New enchantments are 100% stronger.
The other Enchanting perks are optional but it will not harm you to have them if you want to enchant the other pieces of your armor.

Smithing
Daedric Smithing - Can create Daedric armor and weapons at forges, and improve them twice as much.

You get extra damage by doing sneak attacks so you may want to invest some points into sneak.

You also should try this mod:
Skyrim legacy: http://www.nexusmods.com/skyrim/mods/68425/?

Skyrim SE: http://www.nexusmods.com/skyrimspecialedition/mods/1137/?
Thanks to Expired PotatoTomato

and you may want this mod too:
http://www.nexusmods.com/skyrimspecialedition/mods/4407/?

I recommend you to use a full set of Daedric Armor because it has the highest armor rating in the game. Be sure to upgrade your armor to legendary. If you have one you can also use the Blacksmith's Elixir potion to get even higher armor rating. This will not improve the damage done by the gauntlets!
Find the Gloves of the Pugilist. They are located inside of the sewer tunnels beneath Riften known as The Ratway. You can find them on the body of Gian the Fist. Then you disenchant them and cast the spell on your gauntlets and ring. If you have one you can also use the Enchanter's Elixir potion to get better results.
Dragon Aspect shout: Get the shout it will increase your damage. (Dragonborn DLC)
Ring of the Beast - While wearing this ring, you will receive 100 extra health and your claw attacks will do an additional 20 damage. (You need the Dawnguard DLC. It is only available if you choose the Vampire Lord.) You can find the ring in many different locations.

THAT'S IT, HAVE FUN WITH FISTING THE HELL OUT OF YOUR ENEMIES!

If this guide helped you out please leave a thumbs up. =)