There's no doubt that you can get a better system building it yourself at the same budget, but with custom builds come certain risks as well, namely dealing with possible defects, malfunctions, DOAs, and compatibility issues that just doesn't get the machine going as it should. Putting the hardware together is the easy part, which most people talk about, but it's the less talked about part, the software side of things, that give the beginners most trouble. If you are not too certain about figuring things on the monitor and understanding what to do in the BIOS, don't waste your time and just buy your son a pre-built one, it'll come with a warranty so even when it stops working you can simply pick up the phone and yell at the vendor to fix it, and your son will think you are a great powerful man.
Custom building a PC seem very appealing, but nothing is really that easy in life, with pc building comes a lot of studying and information that you have to digest and comprehend, it takes more time than most people are willing to admit to.
Take me for example, I'm very familiar with building custom PCs, but whenever I build one I have to follow up on the latest trends all over again, so I don't get into buying the parts until I do the research for 2 weeks or so.
Beginners have to start somewhere to get their feet wet of course, but I recommend that you do it when you have to build one for YOURSELF, and not your son, so that you'd feel less pressure to deliver, and also able to do it at your own pace. The last thing you'd want to see is your son's disappointed sad face when your novice-built system breaks down just a week later and you have no customer service to fall back on.