@steephie
Start reading sites like Tom's Hardware and AnandTech. That will give you some really good tips and pointers.
For a Gaming PC, most of your $$$ should go into Graphics and RAM, but the rest of the machine can't be shit or you'll have wasted your money on good Graphics/RAM.
Go to Newegg.com, but a machine, and post it here; people can give you their thoughts. Here's the order in which I PCs:
CPU: Get a mid range i5. That will be more than enough processing power to run your games and use your computer and a normal computer.
Motherboard: Buy a Mobo that fits the CPU you picked out. I personally recommend ASUS, although I've heard good things about Gigabyte. Make sure you have at least 4 DIMM (RAM) slots. The more slots, the more DIMM sticks you can buy, which means the same amount of RAM will be cheaper (2x1GB is less than 1x2GB). More slots will often offer some performance increases. Try to avoid a Mobo that has an integrated Graphics card, as you won't be using it and it sometimes fucks things up.
RAM: 8GB (4x2GB) is more than sufficient. Some people like to go RAM crazy, but when you bump up to 16GB (4x4GB), you're spending much more money and you have to ask yourself if the rest of your machine is going to cause bottlenecks, wasting the RAM. I say stick to 8 unless you know it's not enough. All 4 DIMMs must be *IDENTICAL*.
Graphics Card: Buy the most expensive Graphics Card you can while still having enough $$$$ to buy the other components you need. Graphics card should be your biggest investment. Do not buy two Cards and try to connect them via SLI. It's too complicated for your first box. Do not buy "bleeding edge" cards, ie one that *just* came out. Read reviews and find one that many people have said works well.
Storage: If you can afford it, buy a small SSD drive (512GB or less) for your OS and a few high-performance games. Get a enormous HDD for pennies on the dollar compared to SSD. I'm personally a fan of the Seagate Barracuda. 1TB should be fine.
Power Supply: Don't skimp on the Power Supply. Brownouts will fuck your computer up. Google Newegg's Power Supply Calculator to figure out how much Wattage you need. Get something a bit higher so you don't need to worry about power when you upgrade your box.
Case: Absolutely get a full sized tower. It's pretty much a must considering the size of high-end graphics cards. Don't buy a case with doors and flashy lights. That money should be spent on your Graphics Card. Get a simple, sturdy case that has plenty of room for fans. There should be exhaust ports on the front, top, back (not including power supply exhaust), and both sides.
I may have forgotten some things, but that should get you started.
It's really not that hard. As long as you aren't covered in peanut butter while assembling your box and you have a little guidance, you should be fine.