So you just started the game and want some gear that is superior to whatever you can find. There are a few ways. I suggest you do this after the Bleak Falls Barrow starter quest. Go to Whiterun Stables.

1. One handed weapons and bows. Take the carriage to Markarth. Don't enter the city but go down the road to the mine near the town, some npcs should be talking just outside. Take the quest for the forsworn invaders in the other mine. They drop superior 1h swords, 1h axes and bows that are superior to anything you can get for quite a bit. They also drop light armor that is on par with leather armor, except it's much skimpier, advisable for female characters.

2. Heavy armor. Take the carriage to Riften. No need to enter the city, once again. Go to the NE of the town until you get the "house" icon on your HUD, follow it to the house. Outside it there will be a couple of hostile, crappy npcs. Kill them. They wear a heavy armor (just chest piece though) that is on par with orcish and quite a bit before you start finding it in dungeons.