Like others said, I would join a faction or go dungeon delving/bandit killing and loot. Depending on the faction, they will either give away Light or Heavy armor-- for instance, Imperials give you Heavy Armor, while Stormcloaks give away Light. Heavy Armor gives more protection, but makes it hard for sneaking and you move slower as well.
If you don't feel like doing the war related quests first, there are some other factions available. Here is a list of factions that give away armor or have quests where you can obtain some nice armor:
- Companions (located in Whiterun. Heavy Armor)
note: They do not give you armor at first, but you will have access to armor later on.
- Dark Brotherhood (Possible spoiler if I reveal how to find location. Light Armor)
- Imperial Legion (join in Solitude. Heavy Armor)
- Stormcloaks (located in Windhelm. Light Armor)
- Thieves Guild (located in Riften. Light Armor)
--- Nightingales (a sect of the Thieves guild you can join after progression. Light Armor)
Just use what serves you best at the time and your level. Smithing is a great craft to begin working on and investing perks in so you can make your own, better armor. If you're into thievery, spend some time on sneak so you can steal armor from shops and houses.