One of the hard things sometimes with non-linear RPGs is deciding "what to do next". It's a big wasteland and it's not safe out there at all. But for the first few levels, odds are high that you're not going to stray too far from Vault 101. At least not until you grab a few things like gear, guns and growth.

Growth (a.k.a. leveling up)

I talked briefly last time about the suggested order of perks, but now I'm going to examine the first 8 levels of perks / skills and recommend a plan. I'll assume that you only took 5 points in INT, so you'll get 15 additional skill points each level.

Level 2 (exiting from Vault 101)

This is about the one and only time that you should take a +skill boosting perk. Alternately, it might be worth using Intense Training to bump up a sagging SPECIAL attribute. For example, putting a point into INT would give you an additional skill point each level, along with boosting all INT-related skills by a point at the start.

But for the starting player, who are probably focusing on small guns for the first few levels, Gun Nut or boosting your AGI up a point with Intense Training is a very strong choice.

Just make sure that Lockpick, Science and Explosives are all at 25, or that you have gear / chems that can get you to 25. Gear can often give you +5 in a particular skill, while chems like Mentat might only give you 1-2 skill points in that skill.

Level 3

The Black Widow perk is a good choice for female characters, while Lady Killer is more of a stylistic / roleplay choice for males. Alternately take Intense Training and boost up a stat like AGI, Luck, INT or STR.

For skills, I suggest focus on the "big 7": Explosives, Lockpick, Medicine, Repair
Science, Small Guns, and Sneak. You're going to want Lockpick and Science as close to 50 points by level 6 or so, so always put 5-8 points into these two skills each level at the start. But you're also going to need Repair and Small Guns up to 40-50 by level 6 as well. Explosives and Medicine can wait for a bit once you've hit the minimum of 25 points, and you'll have to decide whether to focus on Sneak or not. So you might end up with something like the following at level 3:

25 Explosives (+10 Level 2)
30 Lockpick (+15 GOATS)
25 Medicine (+10 Bobblehead)
35 Repair (+15 GOATS, +5 Gun Nut)
20 Science (+5 Level 2)
30 Small Guns (+15 GOATS, +5 Gun Nut)
30 Sneak (+15 Level 3)

It's not a perfect build, and if you have higher levels of INT you'll have an additional few points each level to invest. And it doesn't count bonuses from armor. After this point, you're almost always going to dump 5 points into Lockpick and Science each level. Which will get you up to 50 points in each by level 6 or 8.

Level 4 (Educated)

There are four interesting perks that show up at level 4: Educated, Child at Heart, Entomologist and Comprehension. However, Education is, hands-down, the strongest of the perks that don't just boost skills. Every level, you'll gain an additional 3 skill points that you can invest in your skills. That's a huge, absolutely huge, and mind boggling large bonus to how quickly you'll work up through the skills. As in, 16-20% faster skill gains.

It's the difference (if you put 5 into Lockpick and Science each level until you get to 50) between only having 5-7 points to distribute to other skills and having 8-10 points to distribute.

Take it, you've love it. It's good for you!

Level 5

Choose between Child at Heart, Entomologist and Comprehension for this level. Or go back and take one of the Level 2 perks. Comprehension is pretty powerful, however, because you'll need to read half as many books to get skill points (you get 2 per book instead of only 1). Child at Heart is an interesting perk that is more roleplay oriented (you get along better with children NPCs). Entomologist is good for dealing with mutated insects, but you'll need to have already raised your Science skill to 40 in order to use it.

By this point, your Science and Lockpick skills should be up to around 35-40.

Level 6 and 7

Toughness is a good perk, if you have your Endurance attribute at 5 or better. Fortune Finder is also tempting for those with 5+ points in Luck. Gunslinger is extremely good for those focusing on pistols or other one-handed weapons. The other perks are either skill boosters or not as useful. Sneaky types will probably end up taking Gunslinger and Fortune Finder.

By this point, your Science and Lockpick skills should be up to around 40-50.

Level 8 and 9

Commando is a huge perk as it grants better accuracy in VATS when using two-handed guns (hunting rifles, assault rifles, etc). You'll likely be running around with one of the 5.56mm or .32 caliber rifles as your primary weapon by this point, so this will make it a lot easier to get off sneak attack criticals rather then missing at long range.

Rad Resistance, Scrounger, and Strong Back are all good choices at this level. Depending on prerequisites, you may only be presented with some of these possible perks.

Science and Lockpick skills should be up to around 50-60. Your primary weapon skill should be at least 50 by now. Hopefully Repair and a few of the other big seven are closing in on 50+ as well.

...

This is the point at which things really start to diverge and you'll want to start focusing on your preferred weapon type (small guns, energy weapons, big guns) and playstyle (thief, sneak, thug, brute, soldier, demolitions, etc).

My planned path for the rest of the levels is as follows:

10: Finesse (higher critical strike chance)
11: Animal Friend (animals now ignore you)
12: Silent Running (you can now run instead of walking)
13: Sniper (higher accuracy for head shots in VATS)
14: Light Step (never set off mines or floor traps)
15: Lawbringer (bring evil to justice for karma and caps)
16: Action Boy/Girl (+25 action points in VATS)
17: Better Criticals (higher crit damage)
18: Concentrated Fire (repeated hits are more accurate)
19: Computer Whiz (never get locked out of computers)
20: Grim Reaper's Spirit (VATS doesn't use AP if you kill your target)