For me, it's a pattern every time. When I leave the vault, I head directly to the house with the girl in it to collect 300 caps. Then, I bee-line straight to Megaton, and talk to Moira, and start the WSG chapter of radiation sickness. I then stand in the puddle outside Megaton while drinking the water. This gives me a useless perk, but it's the easiest to knock out of the way. Then, I accept the food quest.
But rather go to the mart, I head over to the high school and knock some sense out of those young punks. This allows me to acquire some serious leather and rubber armor, and repair it as best as my level allows. I don't mind a few of the knick-knacks lying about (one time, I got a sniper rifle early - high luck perhaps?). From there, I go to the mart and clean it out.
When I return, I'm usually level 2 and I've enough points to get my free house. Then I head off to Minefield to do a little sweeping, and pick up one of my favorite weapons in the game. Comically, I often forget to do one step of this chapter and have to go back!
That's my pattern. From there, it starts to get mixed up, depending on where I want to go. Often, though, I'm usually heading to GNR simply so I can get my radio broadcast up and running. I love running around with the radio on.
Okay, now for a ridiculous question: Has anyone melee'd a Deathclaw before? I'm thinking of giving up guns this time around and going for a strictly melee character. However, I don't want to find out later it was a wasted effort when I can't even beat a DC to death with my melee. Oh, I generally stick with batons, power fists, and brass knuckles, not the bludgeoning weapons in the game. Too slow and heavy.