Pc gamer here. Building will almost always be cheaper, and your budget is plenty. https://pcpartpicker.com/ is your best friend. Figure out if you want to go with Intel, or AMD. After that, pick your CPU, then match a decent motherboard to it. Then, GPU, ram, SSD. Finally a power supply to power all that shit. Obviously you'll need a case, but they can be had pretty cheaply, and one is more or less as good as the next. Pcpartspicker will narrow down your options to only things that are compatible as you build the system. So if you pick an intel cpu right off, it'll only show you intel motherboards, etc. And building it yourself means you can buy stuff used if you want, or shop around. I've built quite a few over the years, and wouldnt have it any other way. Or just say fuck it and buy a prebuilt, and hit the ground running.