Here is an alternative suggestion. This is not intended to be a contradiction of the above post, in fact, the above post is very good for home building.
The alternative is to shop around and investigate locally and see if you can find somebody in your area. That's willing to sell them older gaming computer. They had put together. Usually private individuals will give you better deals on used components than going to a place like eBay and trying to get used material from big companies. One reason for this is that gaming computers tend to be a very small market and the resellers that resell stock computers are interested in a larger market.
Now, having said that, you could do a kind of a hy-bred situation. Perhaps picking up the case and power supply from one source, and then maybe finding a very good motherboard from another source.
If you find somebody that selling a brand name power supply, it probably still has plenty of life left in it. The high-quality power supplies will last for years before they have to be replaced.
As for motherboards, even some made years ago can still be very good. It depends. Gigabyte would be your best choice . The AMD CPUs usually off for more performance for what you paid.
In my opinion, buying from somebody in your own area is a lower risk than trying to buy something by mail order. But that is just my idea. It depends on where you live.
That's all I have to say.