If you pre-ordered through Game Stop and got the classic pack, complete with vault 13 suit, canteen, and 10mm weathered pistol, that pistol actually packs quite a punch, particularly if you get swarmed and need a lot of lead flying through the air. Whatever you do, do NOT modify it, even though it's possible to do so. It's an effective short-range weapon through the early and much of the middle part of the game. Personnally, I like the longer-ranged weapons.
I've hardly ever used the grenade launchers. Even the 40mm only pisses the Deathclaws off.
I picked Shotgun Surgeon as a perk, and picked up the riot shotgun. You can do a lot of damage, especially inside buildings. Don't forget to switch out ammo. Slugs work really well against big targets. I took out the whole herd of Nightkin inside the place where the ghouls are fixin' to go into their eternal reward using the rockets. Stealth boy and slugs are your friends.
Speaking of shotguns, Cass is far and away the best companion. Give her a riot shotgun and whatever ammo she uses (regular shells, I think - she doesn't seem to use any specialty ammo) and watch her go nuts. She makes hunting rifle distance shots with a shotgun. As with all your characters, keep a close eye on the condition of their weapons and amor. Sometimes, nothing seems to degrade, but other times, they use up a specialty weapon and cast it aside. Boone is especially hard on weapons you give him.
Another hint I picked up from the internet is to start out with IN as high as possible (9), and CH as low as possible (1). Having CH that low does not affect interactions, including speech and barter (both more important in this game than previous games), but it does affect a few perks.
Don't take any perk that gives you more experience points. It's a waste of a perk. You'll get to level 30 before you know it, and with a perk coming only every other level up, you should pick them wisely.