There are many ways to start off in Kenshi. One way is to recruit Hired Swords at bars and form your own team right off of the bat. This method will get you off to a quick start but fighting bandits with no combat skills can be challenging.
One other way to start is to head out straight away alone staying slightly near town and finding a band of enemies, lead them back to the town until they attack the guards who will fight with them. You can easily gain experience using the guards as meat shields and attacking from behind. This makes it fairly easy to gain levels and money via looting the weaker items and selling at the town you're at.
Joining the Army has not been implemented yet, but you can still follow the patrols through the desert. This method is a easy way to get experience not only in the game but with the game and its mechanics. Because you will be fighting along with many skilled AI you will not likely die.
Trade is a viable option to increase your income, buy resources in bulk at shops with low markup rates such as rum, building materials, steel bars etc. Then take them to other towns where markup rates are high and sell them off.
It is highly wise to travel with AI patrols at the start, and also good ideas to work on your defense skills while you're with them. You can do this by ticking the block only box on the bottom right interface, this will give you a +20 defense skill bonus.