Build a system off of the AMD Llano (old), Trinity, Richland, or Kaveri family of APUs if you want budget gaming performance. You won't have much fun trying to emulate a Gamecube game on the CPU but the GPUs in them are RIDICULOUSLY competent for the amount of power they draw and the heat they kick off. Even my A6-based laptop handled every game you mentioned on max with ease; an A10 desktop processor will be a loving monster.
Case is obviously up to you, 8GB of RAM is plenty, storage is up to you, and obviously you need an FM2 socketed motherboard
again they're not exactly beefy CPUs but they overclock well and the GPUs are loving ridiculous, they're great for budget gaming