Luck

Luck Training

Luck primarily affects the recharge rate of your critical rates. It has also direct correlation to any random checks like the quality of loot you can find.

Fortune Finder

This perk specifically increases the number of caps you'll find in containers.

Scrounger

This perk allows you to find more ammo from the bodies of enemies as well as container. Since Fusion Cores are included in the Ammo category, this increases the chance of finding more Fusion Cores per container that you normally would.

Bloody Mess

This perk is a must-have for any combatant adventurer, no matter what the build. The damage bonus applies to any type of damage you deal, stacked over the other damage boosting bonuses or perks you have. Plus, you get to see your poor enemies explode into bits and pieces.

Mysterious Stranger

When targeting enemies in VATS, this uncontrollable allied NPC may appear randomly, delivering a single devastating shot from his magnum that will instantly kill your target. His appearance is purely random and you won't have a chance to interact with him. The frequency of his appearance will depend on the rank of this perk.

Idiot Savant

This perk is quite unique in its way. Basically, the lower your character's intelligence, the more EXP you can potentially get with this perk active. For more technical explanation about this perk, please follow this wiki page. Also, since the EXP multiplier is randomly given, you can save your game before turning it in to the quest giver and reload your game until you trigger the EXP multiplier.

Better Criticals

This perk seems to affect only criticals triggered in VATS. Sneak attacks deal critical damage so if you want to further amplify this damage boost, you can go with Ninja and/or Mister Sandman perks.

Critical Banker

This perk allows you to store criticals so you can trigger them manually in situations you need them the most. You have to be in VATS in order to use these stored criticals.

Grim Reaper's Sprint

This perk is a must-have for heavy VATS users. For every kill in VATS, you'll get a chance to recover your entire AP with this perk on. This may go a long way since you can chain kills if you're powerful enough to take out enemies in one or two shots.

Four Leaf Clover

This perk gives you a chance to fill your critical meter for each hit in VATS. This means you'll be able to land critical hits most of the time. If you have the Critical Banker perk as well, this perk helps you fill your critical reserves easily.

Four Leaf Clover

This perk makes enemy projectiles ricochet back to them, instantly killing them. Though the game's description say that the closer you are to death, the greater the chance of this effect from triggering, that still means that there's a chance (albeit smaller) for this effect to trigger.

Images courtesy of Fallout Wikia.