In general, it's best to avoid being seen before you make it to the safety of civilization. If you're spotted, run like hell and you might just escape. Whatever armor you start with, it's not as important as your life (or that sweet Meitou), so if you are being weighed down, just ditch the armor! If you face enslavement or prison before you can escape properly, you might even want to throw the weapon on the ground and come back for it before it despawns.

You might also want to turn your Global Population down to 1 until you're someplace secure.

A Butcher's Favorite Tool: This one is just like The Cannibal Hunters.
Crab on a Stick: Swimming might be your best bet. You can always ditch the armor and carry the pet if you're worried about it.
Fishbait: Keep to the shoreline and dash for the water to avoid combat.
Jitte Out: You're a ninja. Do the Naruto run or whatever.
Pipe Dream: DOOOOOOOODGE!!!
Slave with a Sword: You can actually swim out over the north wall if you're quick enough!
Sole Reaver: Run, before the guards spot you.
Southspear: Your soldier is surprisingly tough, so he'll probably be okay after taking a beating. The Skin Bandits won't bother a hiver if you decide to travel through their territory.
Sunfall: This is the cheesiest of cheesing Kenshi, and the strongest weapon in the game, so I've made it a challenge. You must Assassinate the target by rapidly spamming the command to raise your skill. I myself learned how people do it by testing this mod, so rest assured, it works.
The Emperor's New Sword:Best do all you can to assure the guards don't notice your bounty.
Welcome to My Parlor: RUN AND HIDE.