Here are a few recommendations to consider:
- Save often
- Don't feel like you need to do the Main Quest immediately
- Consider talking to Moira at Craterside Supply about helping her. That quest line provides a great focus to start the game
- Focus on one kill skill. Small guns is probably easiest. Keep in mind you don't need to get it to 100 and there is a bobblehead for each skill that increases it by 10
- Repair is a very important skill
- lockpick can be a very useful and profitable skill
- Scrounge any ammo you can. Particularly at low levels
- Keep your weapon fully loaded and in good repair
- Go to Rivet City early on and the the intelligence bobble head, that will help increase the rate at which you gain skills
- Take the Educated perk early on for more skills (though some would say there are plenty of skill points in the game, I think it's nice to get them early and it's helpful for a first playthrough
- If you go into Vault 106 don't close the door after you enter
- Save often