I'd say you've got a solid start on the basics there!
For things to work on right now, you want to try to focus on getting that walk cycle right.
There's a good visual guide on how they should work here:
You can add or remove frames from it, but this is a good general reference if you want to get it looking good.
This is a great reference, and is actually the one I used myself when animating my first walk cycle a few days ago.
Here is my animation:
I excluded the "high point" frames, but as you can see the cycle still looks alright without it. Of course it'd look better with animated arms.
OP, if these animations are for a game, I would suggest doing first just the basic animations (idle, walk, jump, shoot). More complex animations aren't necessary and can be added in later. Things like a reload animation can be substituted with a reload sound, for example. It's important when venturing into a new territory (pixel animation), to keep it simple at first and manageable in order to not get discouraged and lose motivation.
This is speaking from experience.
Good luck on your game and your pixel art'ing, OP!
