New computer.

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First, I recommend educating yourself. This article is pretty solid, it teaches you everything you need to know about computers. The next and probably most difficult and time consuming stuff step is searching for parts online (I don't like pre-built PCs but I suppose there are good deals out there if you can find them). Visit all of the computer stores' websites you can find (or order from Amazon or something if you want). Go through all of the essential parts one by one and via a process of elimination find the part that best suits your needs (one you can afford and isn't excessive). It will take a while but there are sites out there that offer comparisons on CPUs, GPUs, motherboards and everything you can think of. There are especially a lot of sites that compare GPUs, that often test the newest games and report the average and high/low FPS for each GPU. It's actually quite a lot of fun though, so take your time and don't rush into anything. Here are some general guidelines that you should probably follow when looking at parts:

CPU (processor): For gaming you probably want a quad-core but if you have money to spend you can buy more insane CPUs but most of them are too excessive for gaming purposes. Check the clock rate that's listed; above 3.0 is fairly solid, anything below 2.0 is usually not going to cut it for modern games.

RAM (memory): I don't recommend anything below 4 GB. 8 GB is fairly solid, and only go for 16 and above if you're into hardcore modeling or sound design/mixing/whatever.

Motherboard: Just make sure it's compatible with everything else you buy. If you purchase the parts at a retail store someone there can help you out. As I said, educate yourself and you will know whether the motherboard suits your purposes.

GPU (graphics card): If you can afford it, buy the latest model from whatever company you prefer. These things become outdatedreally fast, but just make sure it works well with the games you're going to be playing. It will certainly last but if you are big on playing the newest games when they come out prepare to upgrade often, and you may possibly need to buy an extra one (not usually necessary).

PSU (power supply): 500W is solid, and 700W and above is only necessary if you're going to build a crazy rig (dual GPUs and such). Whatever you do, don't cheap out on the PSU. While there are safeguards on most modern motherboards that protect against power failure if the PSU goes out with a bang it very well may take everything else down with it. It's just not worth the money you save. Buy a good one.

Hard drive: You probably know how important it is to have a lot of space. Anything under 500 GB nowadays is probably not a good idea. If you have an external place to store your stuff, you may want to consider buying a small SDD. I have one that is around 120 GB and it works beautifully. The system boots in literally 3 seconds and SDDs carry with them a bunch of cool features. There are articles online that explain how awesome they are, but they are not really necessary as they are quite expensive as of now.

Everything else like peripherals and such is up to you. I don't really know any good screens. Just buy whatever has good reviews and supports the resolution you want.

P.S. Probably some of my info is old. I don't really keep up with the newest trends that much so depending on your preferences you may want to go much higher than what I recommended. As I said, read up on it yourself and make educated assessments when searching online.