Head to Riverwood, then to White run, then to the first barrow. Don't take the golden claw back to the guy in Riverwood, use it to go further into the barrow. Remember, examining items gives clues and passwords to open doors etc.
And remember- ALWAYS steal. Learn how the "Spotted" icon works and always steal healing potions and weapons from dealers. Buying is for suckers. Level up your sneak to make it easier. And level your smithing! You can start right away in riverwood! ALso, cool as it is, don't use destruction magic as your main weapon as it scales poorly through the game. MAx archery and hand to hand combat and learn how to enchant, disenchant, and re-enchant weapons. ANd use soul gems. And read books. There are books everywhere. All contain useful lore. And avoid giants until you level up they will crush you.
Do the Companions missions (the house that looks like an upside down boat in Whiterun) early in the game. You get a great weapon, a great morph ability, and you level up with easy missions early.
Go forth! Dragonborn!