I've changed some of my thinking on skills and perks for the first 8-10 levels. See Getting started (Baby Steps) for a discussion of SPECIAL attributes and Age 16 and the infamous GOAT for a discussion of Perks.

Level 2 and 3: Don't take a skill-boosting perk here. It's not worth it at all. Take either Black Widow / Lady Killer, which is excellent for females but not so good for males, Swift Learner (10% faster XP gains), or Intense Training (to boost a SPECIAL attribute).

For females, Black Widow is a good one combined with Intense Training. For males, I'd probably take two Intense Training perks (at level 2 & 3). I'd suggest boosting Luck or Agility if you're a VATS user, or maybe Strength if you went light on it at the start. Or make sure that Endurance is at 5+ so that you can take Toughness at level 6 or 7.

The "big 7" skills still matter here for a small guns / stealth character. All of these need to be at least 25 at level 2. Science, Lockpick and Repair can be left at 20 as long as you have +5 gear that you can equip when you need to.

Explosives
Lockpick
Medicine
Repair
Science
Small Guns
Sneak

Level 4: Take Educated. Those extra 3 skill points at each level are wonderful.

Level 5: Choose between Child at Heart, Entomologist and Comprehension for this level. If skills are your obsession, choose Comprehension. If you think you're going to roleplay a more childlike mindset, go with Child at Heart (which opens up unique dialog options when talking to children).

Level 6 and 7: Small gun types will take Gunslinger at 6. For beefier types with Endurance of 5+, Toughness is a strong choice as it gives you 10% to overall Damage Resistance. For a soldier / commando type, Toughness is very much a must-have perk. Demolition Expert is a runner-up, the 20% extra damage with explosives can come in handy (grenades, mines), but you'll need to have boosted Explosives to 50 points.

(A lot of times, Toughness and Demolition Expert end up as backfill perks later on. If you took points out of Endurance at the start, a lot of times you'll have to take Intense Training at level 7, or backfill.)

Level 8 and 9: Commando for the small gun types, Scrounger, Rad Resistance or Strong Back for others. Note that Strong Back requires both Strength and Endurance to be 5+.

(I much prefer the Scrounger perk over Fortune Finder.)

Level 10 and 11: Take Finesse for a higher critical hit chance. The other choices range from amusing to funny (Mysterious Stranger, Nerd Rage) or selectively useful (Mister Sandman). Here and Now immediately boosts you to the next level and is basically free XP.