When I start as a peasant, I put all points in my RL Patience skill and...
Well, kidding. But I take novice WeaponSkill/Armor/Shield/Dodge/Wrestle/Throw/Fighter, and sometimes swimming.
For attribs, I take 1 Strength/Agility/Toughness.
You can train anything, but as a peasant, don't go to doing the quests right on: your guy is just some farmer that watched Karate Dwarven-Kid and now thinks he can take on Dragons.
Go kill some wildlife. You probably started with a dagger (or something), use this to 't'hrow it into wildlife. With luck, you can hit something that will slow them down, and allow you to get close.
When you do, wrestle them as much as you can. Try breaking their legs/arms/paws so they can't do much, and will probably fall uncouscious.
After this, you can grab their throat and strangle them until they die: this will give you a lot of wrestling exp.
Remember that you need to 'p'ut your weapon/shield into your backpack to be able to use your hands for wrestling.
Wrestling and throwing will help your character a lot in combat.
You can also 'S'neak around to train Ambusher, and try Swimming to gain even more attribs (which are more important than skills, most of the time).
If you took no swimming skill: Go to the beach, go down a beach ramp and it will tell you you're drowning. "Swim" around sometimes and go back up the ramp, repeat. Soon you'll get Novice Swimming, and it'll be easier to train the skill, which gives you some atrib gains.
Check the wiki's Adventurer Mode page and look for the attribs and skills, you'll see which atribs affect each skills, etc. I just read it today and learned things I didn't know of, and I play the game for around 3 years now... (I'm a lazy ass Dorf)
Huge text, hope it helps anyway.