I don't think you realize what you are throwing yourself into. How much research have you done? It would be smart to to do some before you go and spend money or waste time with mock builds. If you are asking what software to use, I assume next to none which is a big problem for such a complex task such as this. But I'll start you off with a simple breakdown.
Hardware/software is actually pretty straight forward. If you play games (of course you do) it's easy to tell what engine they use, there is usually the logo popping up when starting the game. Most everything 3D would be modeled in max or maya. I should also mention zbrush for polysculpting more detail. Textures and 2D games would be photoshop though most flash games just done in flash. Unity, cryengine, and unreal are free for non commercial use. As for free alternatives to content creation, use gimp and blender.
Both builds presented so far don't really fit the bill. The first being...well that's not a game dev rig, maybe a cad build with a cpu renderer, which is the wrong industry. And the second is probably too far above the $1200 budget. Although you really weren't exact on if you needed monitors/os/reusing parts, just fill this out http://www.tomshardware.com/forum/261222-31-build-advice.
Nothing really needs a powerful cpu, except for one thing and that is lightmap baking (for 3D games); if it does use the cpu since some could use gpu. But just fyi, high end games using cryengine, unreal, frostbite, etc, no longer use pre baked lightmaps. There really is no point in a workstation card in this field. The extra features are unnecessary and the game is going to be run on gaming cards so they are developed using gaming cards. Something like a low end v4900 will just limit you to low end low poly games. Though 2D games really don't need much of a pc at all. Generally speaking if your pc can play the type of games you want to develop, you can develop those games on that pc just fine.
This is just the art aspect, if you are attempting this on your own, good luck learning to program too. Since you are just learning, I hope you realize how long it takes to actually develop games. And just some advice to end on, making mods for existing games would be a good way to get your feet wet.