For that style of artwork, Adobe Illustrator is probably the best choice, at least for the initial line work. The only issue with using Illustrator is that it's not really an animation tool, so there's very little in the way of onion skinning and other features normally used when animating.
However — given you're a programmer — if you set up your Illustrator document to be a sprite sheet, you could export the entire sheet and do animation playback testing with a little bit of code. You'll probably want the final sprites to be set up as a texture atlas anyway.
If you wanted some more powerful painting features, you could do the initial line work in Illustrator, then take all the paths over to Photoshop for some extra colour work and effects.
Another option would be Flash Professional. It is an animation tool, but not one I like. I'm less familiar with how you'd get all the final assets out of Flash.
So... Illustrator for the bulk of the work would be the way I'd approach it.