This is a frequent question which have a simple answer: You can do both.

But let explain it because it depends of what kind of paint do you use:

What kind of paint can I use to paint Fimo?

If you use Chalk Painting Crayon you can do it before without problems. Same if you use oil paint (although may not dry completely).

However, if you use acrylic paint maybe you should do it after baked the piece. The only reason is because is probable that you have some trouble getting rid of the water of the paint because wouldn’t evaporated completely (acrylic paints are water based) and the consequences would be that could be form bubbles on the surface after baking it.

But it have an easy solution:

Once your piece is painted, wait a few days until the water is completely evaporated and then you can bake it without problems.

Don’t forget that Fimo offers a lot of variety of colours that you can mix to turn them into other colours.