Hi,
The design is intricate for a really basic spaceship!
Okay, so judging from the perspective and shape of the ship, I'm reminded of Dodonpachi. What's good is that you've tried putting highlights in where it hits edges, so you've got the right idea. Overall, it could do with more contrast in the mid range.
My edit:
I made the ship Dodonpachi style.
The thing about this style is that it works with straight lines and diagonal lines, with very few exceptions. This makes shading easier, as everything is straight.
The colour palette is a lot more subdued, going into the greys. This style works with mechanical bits being spread out on the machines like patterns in a patchwork, which also done in the Star Wars franchise for its spaceship designs.
The lighting comes from the top-back, highlighting the edges, and making the sides and the face closer to us darker.
I would say the way you can build designs in this style is like an architect's elevation drawing, where you start with a surface which is extruded, and thus becomes a 3D shape.
In terms of palette, if you want to do "purist" pixel art, you should avoid transparent brushes and brushes with anti-alias or a smoothing option on: this way you don't end up adding a lot more colours accidentally. You also have to consider where you can re-use colours rather than picking new ones, so it's important to keep track of the colours you've used.
Optimising colour palettes really depends on what you want to optimise the sprite for: visibility (high contrast compared to background), readability (high contrast within the sprite), the mood (ex: if the game happens underwater, things tend to have some blue colour in them), and the textures in the sprite (ex: imitating wood is not the same as imitating stone).
Otherwise, you can do indexed digital art, where you use any kind of brush and/or layer mode you want, and the index the colours in the image - this reduces the colours to either a default colour palette, or a palette of your choice.
Hope this helps.