Right now the best budget CPU for gaming is the i3-6100, pair it with a decent motherboard so you can have a good upgrade path and expandability like Gigabyte GA-Z170M-D3H. Although it's about $30 more than budget boards, you get a good chipset and dual PCIe slots so if one happens to go bad (which does happen) you can move the video card to the second one without replacing the full board.
Make sure you get a quality power supply also, Seasonc M12II are good models and reasonably priced. Modular will get you a neater looking setup.
For a case, I like the Phanteks models, they have very good interior design, although can be pretty large. I bough the Enthoo Pro M model and although it's not very tall, it's long...