Overall a good start.
I'd suggest to reduce the amount of shades for sprites with a low resolution.
Otherwise, what will often happen is a form of banding, pillowshading or overall blur.

I changed his pose just slightly, and got rid of his fingers.
Also adjusted the lighting, to get a more uniform look.


One more thing you might wanna check out is his pose. It is not a typical spiderman pose. you could also go for his web shooting gesture \m/ to get a more iconic spidey.