Your process is more or less what I tried to do.
1. Outline. I didn't save the actual initial outline so this one is recreated by retracing over the first edition. I didn't know exactly where the arms would begin and end or how wide they would be, I was basically just going for the right silhouette.
2. Initial coloring. I can't find the exact reference image I was using to show you, but the coat I'm trying to go for looks something like
https://images-na.ssl-images-amazon.com/images/I/41B0Y3FNQ8L.jpg but a little darker gray. I completely missed the boots, they were supposed to be changed to near black at some point.
3. Shading. Add a color darker than the helmet, and one in between the helmet and the coat because using the helmet gray seems to add too much contrast. The flaps have no real way to differentiate themselves from the rest of the coat besides shading, and it isn't obvious why those pixels are there so I just change their color, now they look more in place. Add shading on them anyways.
4. Highlights. Added one color for coat highlights, grand total is 5 grays between the helmet and the coat.
5. Revision 1. Lighting on helmet is bad and shape is off, fixed. Highlight on helmet looks really bizarre and out of place, removed. Shading on flaps make them look bigger than intended and doesn't seem worth it, advised to keep details to a minimum so removed. Highlight on legs seems too bright and out of place (like the helmet), removed. Increased the size of other shadows and highlights to make them more obvious. Try to increase contrast in facial colors. Colors are too gray, add a little blue to most of them, red on the dark part of the helmet. To minimize colors, lightened up on the helmet and made the edge of the front flap of the coat the same as the shading color for the coat, making 4 gray/blues.
6. Revision 2. Revise boots. Add more saturation to add color. Dark red shade on helmet now clashes heavily with the blue, changed to dark blue instead. Keep red for the boots because using the blue on the boots looks really dumb. Use blue on shading for boots to avoid adding more colors.
That was my thought process. I noticed in your sprites there's a large highlight on the helmet on both, basically eliminating the base color in favor of a shadow and highlight color. Your second sprite also seem to have darker darks and brighter brights, I suppose that ties into contrast but I think the shape of your sprites and angle of the lighting helps to where you can fit all the colors within three pixels of each other in a lot of spots. Also the angle of lighting on your edit of my sprite doesn't quite seem to be consistent. His arm makes it look like he's lighted from the left but his helmet has highlights suggesting it's coming from the right.
But overall I think my pose is ok. There's nothing specifically wrong with yours and the lines are at nice angles but I'd rather have the butt of the gun be pointing to his shoulder rather than stuck under it. My colors could probably use some work in being more colorful and helping identify specific parts of the sprite but since they're all supposed to be the same gray my options are limited mostly to shading.