Mention perks that were added to the FNV and its DLCs, not taken from any of the previous games.

I would say Jury rigging is the best new perk. A very original and useful perk.

For the worst, i'll say Nuka Chemist. I think this perk shouldnt have existed and instead should have been added to survival skill.

Nuka Chemist is from Fallout 3 just called quantum chemist, you make quantums. Anyways with Gun Runners Arsenal nuka-chemist becomes useful as you can make more nuka-cola quartz to make nuka-grenades, which are amazing.

The long haul perk

Best: Demo Expert
Worst: Light Touch

Jury Rigging is more convenient than necessary. You can totally get by without it by using weapon repair kits and repairing your armor at the NCR outpost with Major Knight.
I actually never use jury rigging on weapons cause weapon repair kits are so abundant via Dead Money and crafting, all it does is save you some time to traveling to the outpost to repair your armor.

The best perks are easily Better Criticals and Just Lucky I'm Alive. Each of these perks add +50% critical damage. If I could only have one perk the entire game it would be Just Lucky I'm Alive......immune to critical hits and +50% damage is all your really need.

It means the difference between killing your opponent in one shot or three.