I've been practicing my sprite art all in GraphicsGale, it's a wonderful little program that's absolutely usable for free. Even if you need to make a GIF out of it, you can always use GIMP. Besides being the open-source equivalent of Photoshop, GIMP is also excellent at editing GIFs (albeit a little bit counter-intuitive, but once you get the hang of it you can set individual frames' delays and animate it as you see it in GraphicsGale).
If you're making a fangame, a good starting point is the old 8.1 version of Game Maker. Studio is garbage lemme tell ya what so don't get that. Game Maker will ease you into programming but still let you go wild whenever you want. You can straight up code the game yourself, benefiting from GM's hundreds of built-in functions, or use the drag and drop interface to pseudo-program your game.
Personally for game design I've switched to LOVE2D, which is a bit like Game Maker except you program your game from scratch in Lua. It's awfully advanced and requires a lot of backbone work before you can just jump right in throwing enemies and players about, but it really pays off in the end. Oh, and unlike Game Maker, it's free. Free free.