If you like quests, then...I tell new players this a lot: at level 1, you get decent xp from poo. It cuts in half at level 2, but you don't need ammo to shovel poo so do poo til 2. Then start doing the easier jobs like moving boxes and water for farmers. Then easier quests like Sad Wife, Wasteland Band, the deal for Jacob, all available in Hub, and easy at any level. Delivery message for Elmer in Necropolis, Tent in the Wasteland, Medical Investigation (Vault City), not necessarily in that order.
Don't fight much with gun skill less than 100, but once you get gun skill over 110 or 120 or better, fine - get the scorpion cave quest from the doctor in Junktown (for non-melee) and don't get stung.
Remember though: to get a free boost to your fighting skill, get Boneyard Guard early, before you've boosted any of your fighting skills.
Once you get Even Tougher at level 9, or at least Toughness at level 6, get your Carry Weight perks, and try the ant lair quest in San Francisco, and the dogs quest in New Adytum. You can try the Rail Line Gang later with more hit points and i recommend drugs (Psycho) for that one.
You can also try the first part of the tanker quest from Klamath at a fairly low level, but you'll likely need help with the boss robot at the end. The Gunrunners mutant cave quest is a tougher one, lots-o-fun for the whole family (so bring them).
With a little crafting and fighting a few random encounters along the way, i usually make it to level 9 doing the easier ones.