Lasso tools and paint fill for basic colors first. Then I find a color of a similar value (only slightly darker or lighter) but either to the left or right of the color wheel (so if using yellow, go either orange or green depending upon the type of lighting the panel is using) and then I set a gradient for that object. Subtle gradients I've found make a big difference.
This same technique is good for your shadow layer too (I usually have a multiply layer set to a low opacity)- rather than have flat shadows, set a gradient from a lighter edge to a darker edge (shadows are often darker closer to light sources).
I also tend to have the lineart set to multiply and around 90% in opacity to absorb the color underneath and not look so stark and black against the colors. It definitely softens the lines up.