There are so many things you can use to color soap.
You can use herbs, powdered spices, clays, micas, ultramarines, oxides, liquid color, fd&c colorants, and more.
Some are 100% natural, some are sort of natural or claim to be naturally derived and some are artificial. It may help you narrow down the choices if you decide how much "natural" means to you.
On the natural/more natural side, (and also cheap) one really easy thing to start with is cocoa powder. You don't even have to measure you can just eyeball it. Mix it in at trace or before when it's well blended. You could easily make a pretty, rustic looking bar with a brown cocoa powder on the bottom and a white layer on top.
You can also make speckled bars easily by adding a little ground coffee or some paprika or curry powder.
I like clays..things like pink and french green clay are affordable and really easy to use. The color of your finished bar is pretty true to how the clay looks in the container. You don't need to be very precise you can just spoon in a couple of tbs or more or less after your soap is emulsified.
One of the downsides to choosing natural colorants is that some colors are impossible or challenging to achieve, for instance, hot pink, fuscia, anything neon,purple is hard, blue almost impossible (altough i saw some soap on etsy recently made with russian blue clay that looked really pretty.)