59, as a colour count is too large for a piece of this size, so my first advice is that you should use limited palettes (6 to 16 colours to start), that way you will further your knowledge in colours a lot (also you could search tutorials on creating palettes, theres one done in pixeljoint by the great sy0sa which is pure gold). A different way to improve in working with palettes is to work with predetermined ones, if you search palettes at google it shouldnt be difficult to find an interesting one (ex: pico8).
Another technique really helpful to start is to work with outline so you dont have to mess with backgrounds and similar shit at first.
P.D.: wich software are you using?