Even though computers are getting less expensive, most gaming systems are going to cost more than your price range as a result of the more expensive video cards and higher resolution screens that are typically part of a gaming system. So "a system that covers everything" and runs everything
well at high settings may not be possible on your budget unless you buy a desktop instead of a notebook.
However, you can purchase a system that runs most games
well at high settings and will run the rest at medium settings. For that, I could recommend something like the Lenovo Ideapad Y570 [link to the Lenovo on Newegg.com]
. The most important thing with gaming systems is the video card and the Lenovo I mentioned has a very good video card for the price range.
Before you buy a new computer, though, there's something else that you may need to consider. If
the games your son plays are all online and you do not have a high speed internet connection (anything equal to or faster than 2 Mbps download / 1 Mbps upload or better qualifies as high speed for this purpose), there will be a lag in that situation as well. A lag in connection can only be fixed by upgrading your internet connection speed and it has nothing to do with the computer. If you already have a high-speed internet connection or if your son isn't playing games online, you can ignore this last bit. But just in case, I wanted to let you know.