For the last thirty years, it has always cost about US$2000 to build the best personal computer you need using current technology. Of course you can always spend more money, but it is unlikely you will need to. The extra cost will be for "bragging rights" more than for any improved and useful performance. For on-line gaming, you will find the Internet connection speed is your main performance limitation... unless you live in Japan or Taiwan where everyone expects warp speeds equal to or greater than one gigabit per second.
The cost of the case has always been roughly one to ten percent of the total cost, rising somewhat in recent years as people began to appreciate the advantages of sturdy powder-coated steel versus aluminum construction. Most desktop cases feature multiple internal fans for cooling, plug-and-play bays for hard-disk drives and optical disk drives or (gasp!) floppy-disk drives and even cartridge tape drives. Most case manufacturers also incorporate front panel access to a reset button, audio jacks, and USB connectors via a cable you plug into the motherboard (mobo).
The choice of mobo can be critical to on-line gaming. Do a LOT of on-line research at various gaming forums and see what the current, latest-and-greatest mobo value is. Best value is not necessarily the highest performing or the least expensive mobo. Rely on the experience of other gamers for suggestions. The life-expectancy of a modern mobo can be measured in years (or even decades), but the technology it incorporates will be "obsolete" before you even take delivery. Manufacturers are constantly making new mobo versions to take advantage of the latest technology. It is impossible to keep up and foolish to even try.
Good luck with your build! I always get a thrill from a new computer build when the BIOS boots up for the first time.