Perks are only given on even levels (2, 4, 6, etc.). Level requirement is shown after the name.
This analysis is based on playing non-Hardcore and non-Melee and NOT using Energy Weapons.
Stims and other drugs, Ammo, and Money are all plentiful, so Perks related to them are less important.
With Boone and ED-E (or other companions) to help in fights, there’s not much need for fighting-boosting Perks.
Perks letting you carry more are not needed. I let Boone and ED-E do the heavy lifting.

The above types of Perks are not listed here for the reasons stated above.

Black Widow/Lady Killer/Cherchez La Femme/Confirmed Bachelor:
I tried Confirmed Bachelor to start in Goodsprings for the 10% damage bonus when fighting the Powder Gang, with the idea of changing to a better perk on the final setup when leaving Goodsprings. I couldn’t tell any improvement in killing the gang members and decided the Swift Learner was better because it gives +10% when XP is earned.

Friend of the Night (2): (Eyes adjust quickly to low-light.) This sounds good in theory since you have to deal with a lot of low-light conditions in the game, but the improvement is very marginal – nowhere near as bright as Cateye. Instead, turn up brightness under Settings and/or on your TV.

Hunter (2): 75% more critical damage against animals. This may be nice to have against Deathclaws, but that comes much, much later. Don’t know why it’s level 2.

Intense Training (2): Pick a SPECIAL to increase by 1. You can select this up to 10 times. An alternative is to buy Implants at the Medical Clinic, particularly since you eventually get more caps than you can spend. However, if you have reached the limit for implants, this perk is your only choice.

Retention (2): (INT 5) Skill magazines last 3x longer. This might be handy once you get the Voracious Reader perk on level 22 since you can freely use magazines (such as Guns and Bullets) to boost your fighting ability, but by level 22, my Guns and other essential skills are already very high.

Swift Learner (2): (INT 4) You gain 10% bonus whenever you earn XP points. Select up to 3 times. Finally a Perk which is good to have on level 2. You level up faster, adding points to your Skills faster, and getting more Perks faster. After getting this on level 2, I get Comprehension on level 4, then this again on levels 6 and 8.

Comprehension (4): (INT 4) +4 permanent points for Skill Books, +20 temp. points for Skill Magazines. You get to level 4 pretty quickly (you’re 3 when you leave Goodsprings), so save the books from Goodsprings and Sloan until you get this Perk.

Educated (4): Get 2 more skill points every time you advance in level. Since it’s more important to get Comprehension on level 4, you can’t get this one until level 6. My impression is that leveling up faster with Swift Learner is more beneficial than getting 2 extra skill points for each level, so I put this off until level 10. I wouldn’t have a problem with getting it on level 6 or 8 though.

Bloody Mess (6): +5% damage, violent animations. For fun only. 5% damage won’t help much.

Demolition Expert (6): (Expl. 50) +20% damage with explosives. I use the Grenade Rifle often against the Legion who are otherwise very hard to kill. I also get a Missile Launcher when it becomes available. You can take Demo Expert 3 times for a total 60% boost.

Shotgun Surgeon (6): (Guns 45) Other guns do the job just as good or better.

The Professional (6): (Sneak 70 – Really?) Sneak attacks with hand guns do +20% damage. This helps with the first shot, but then what? Demolition gives +20% damage with every shot of a Grenade Rifle, Missile Launcher, etc.

Toughness (6): (END 5, take twice) +3 Damage Threshold. I get the DT implant and select a different Perk.

Here And Now (10): Instantly level up. This made sense in Fallout 3 because every time you leveled up, you got to choose a new perk too. In FONV, the next level does not include a perk, so you just lose out on one and they are scarce enough.

Night Person (10): +2 INT and +2 PER between 6 p.m. and 6 a.m. Some people think that this is good because it can help offset the night time penalty of Early Bird, but you can almost always Wait or - even better - sleep in your owned bed at night. The very rare exception is not worth a Perk.

Sniper (12): (PER 6, AGI 6) 25% more likely to hit the head in VATS. Not too bad, but I like to snipe by eye beyond the normal range of VATS.

Splash Damage (12): (Explosives 70) 25% larger area of affect. Could be good after getting Demolition levels 1-3.

Center of Mass (14): (Guns 70) +15% damage when targeting the torso in VATS. Not bad when you also consider that in VATS, the torso usually has a much higher % than the head.

Light Step (14): (PER 6, AGI 6) You don’t trip floor traps or mines. I always get this in FO3, but for some reason, floor traps/mines don’t seem as bad in FONV. Also, I save often and am willing to back up if I get careless. If there is bedding around, I can always sleep off the damage if no enemies are around.

Action Boy/Girl (16): (AGI 6) +15 Action Points. Not a terrible choice, but I usually want something else more..

Tag (16): Select a Skill to increase by 15 points. By level 16, using the Skill Requirements Guide, my Skill points are already where they need to be.

Computer Whiz and Infiltrator are worthless. Instead, just save before cracking a lock or hacking a computer.

Explorer (20): Shows all locations on the map. This is nice to have when you've done the main missions and want to roam around without the inconvenience of having to look at an external source.

Grim Reaper’s Sprint (20): This was better in FO3 because all your AP was restored instead of just 20.

Voracious Reader (22): (INT 7) Comes with the Lonesome Road add-on. It lets you make Skill magazines out of damaged/ruined/burnt books and Wonderglue. At level 22, my most-used skills are already on 80, but with the Comprehension perk and a skill magazine, I can get them to 100. For more info, see Voracious Reader.