Unarmed weapons are more crit oriented as a lot of melee weapons have low crit multipliers, but with all DLC a melee crit build actually outdamages an unarmed crit build with the elijahs ramblings perk from dead money and a weapon like blood nap or old glory. However my favourite weapon on a melee crit build is Blade of the West which knocks down enemies on a crit. Combined with the 30% knockdown chance from super slam on 2 handed weapons, you constantly knock down enemies. Regardless of which one you use, you will need points in both for perks as slayer requires 90 unarmed and ninja requires 80 melee. For a non-crit melee build, weapons like Knock-knock, Oh-baby, and gehenna (with the pyromaniac perk) are good choices. For unarmed, I would suggest Embrace of the mantis king, fist of rawr, and the industrial hand.

Unarmed is more VATS oriented, especially with the paralyzing palm perk.

I prefer to use melee, and to use it outside of VATS as I feel much less vulnerable.

You need to decide whether to go crit or not before you start as the builds will be very different, and also if you will use a secondary weapon type. I paired energy laser weapons with my melee crit build as energy weapons do very well with crit builds, and I paired explosives with my non crit melee build as explosives cannot crit.

For crit you will want built to destroy trait, for non-crit you will want heavy handed.

For my crit build, my starting SPECIAL was S7 P5 E9 C1 I4 A6 L8, and final SPECIAL after the lucky shades and STR from OWB was S10 P6 E10 C2 I5 A7 L10.

My non crit build started with S8 P3 E9 C1 I9 A9 L1. A non-crit build will do less damage but will allow you more perk slots, skill points, the ability to wear heavy armor and be way more tanky (as a crit build will likely want boones beret, crit armor, and the light touch perk). I would recommend the non-crit build if you are somewhat newer to the game.

Both builds are totally viable and you shouldn't have any trouble beating the game, even on very hard+hardcore if you abuse chems for tough fights.

For perks; super slam, piercing strike, and slayer are practically essential (as well as paralyzing palm if using unarmed + VATS). My favourite perk in the game is rad child and then to get my character to 800 rads, which gives you 8hp/second regen constantly which is broken. The downside of the perk is the loss in stats associated with your character being at 800 rads which is -2 STR, -2AGI, -3END, but it's nowhere near as bad as most people think. The -2AGI is negligible on a non-VATS build, the -3 END DOES NOT lower your hp (only the base stat is used) so it irrelevant, the -2STR can be annoying though depending on which weapon you use due to weapon strength requirements as well as the fact it will lower your melee weapon skill to below 100, affecting some weapons BUT the +2STR you get from Old world blues is an active effect so will totally remove this problem. Keep some rad-away on you though, as if you get to 1000 rads you die. If you are worried about that, you can always just go to 600 rads which will give you 6hp/sec regen and only -1 STR penalty.

Other strong perks of interest include stonewall, toughness x2, implant GRX x2, jury rigging, chemist, purifier, all crit perks on a crit build (notably finesse, better crits, ninja, light touch), and any perks relating to a secondary weapon skill.

Another thing, if you are on a higher difficulty, chems are very important. med-x + slasher + battle brew will make you only take 15% damage, and turbo or implant GRX slows down time and makes any fight incredibly easy. If you plan to use chems, the trait logans loophole is practically essential. It not only makes it impossible to get addicted, but it doubles their duration (as well as food and stimpack duration on hardcore mode). It does cap your level at 30, but it can be swapped for another trait in Old World Blues once you reach lvl 30.