You already have the subs so, too late there but, consider this before you buy an amplifier....
That Alpine amp is the best selling amplifier in the country, by a pretty good margin. Now at first blush, that sounds pretty good but not so much so once you think a little deeper into it. Since Alpine sells so many of those amps, then it stands to reason that we would see a lot of them at car audio competitions, right? After all, if I wan't quality, I don't want to know what my accountant neighbor uses, I want to know what the pros use.
You can visit a few car audio competitions or, even easier, you can surf Youtube and see clips from the winning runs of myriad competitors. You won't see many Alpine, Kicker or JL Audio amps in the vehicles with the trophies beside them, if you see any. What you will see is the brands mentioned above by others, along with CT Sounds, Crescendo, RD, Incriminator Audio and a few others.
As an example, the Alpine amp you mentioned does 500 watts at 2Ω. It doesn't like 1Ω and, it's $200.00 and it is rated at 14.4 volts, which is the highest voltage most cars will produce. For a little less money, the CT Sounds 500.1 is rated at 600 watts at 1Ω and 12.8 volts. This means that once you actually install it and use it with the car running, you're going to be getting even more power from it. Most likely ~725 watts. And it's stable down to .5Ω, so a 1Ω load at full tilt isn't going to be stressing the amp at all. It also has tiffany style rcas, which provide both a very secure signal path as well as a very impact resistant connection. It is also strappable, so when your son gets ready for more power, you don't have to scrap it or sell it on the cheap. You just buy another 500.1, strap the two and viola, you've doubled your power with little more out of pocket expense and the two amps will work together like one. Moreover, that amp has a volt meter, a clipping indicator, a power light and an on/off switch on the bass knob.
Lastly, it has a 1 year no questions asked warranty. All that for less money than the most popular amp in the US.