For $600 here is what I would do if it were me. I would get him a really good snare, one that he wants. Let him pick, and if it is $300, then it's $300. Buy nothing under $200. Worldmax makes a great brass snare for under $300. Black Dawg. There is nothing in this world like a good brass snare drum. That snare will last him much longer (his lifetime probably if he keeps it and cares for it) and serve him better than a mediocre snare with a mediocre kit (if you buy the Pacific).
Remember he is hitting the snare and cymbals more than anything else. Maybe look at a pro set of hihats as well. Even used Zildjian New Beats ($150-225 ebay) would be really good. Try craigslist in your area too.
The bass and toms while not great, will be just fine with some really good heads.
For the toms let's go with Remo Diplomat (white or clear) bottom heads on the toms, and depending on whether he wants a jazzier sounding kit go with Remo Coated Ambassadors on the tops of the smaller toms, and a Coated Emperor on the floor tom. If he wants rock, then go with Evans EC2 or equivalent on all toms.
While l am at it Pinstripes and Hydraulic heads are not equivalent. Remo Emperors, Pinstripes, and G2 and EC2 are not 'oil-filled' heads.
Bass drums - I would suggest one of the premuffled bass drum systems. Go to your local drum shop and buy what they suggest. EMAD, Superkick II, my preference is Remo's Coated Powerstroke III batter.
If you have to travel to a bigger city (closest one for me is in Columbus and I am in Cincinnati) take him and he will be in hog heaven. I am talking about a real drum shop, not Guitar Center or Sam Ash. I know a new kit is cool, but my suggestions will sound better than a new kit will.
If you can, either get him some Rock N Wraps or make them yourself if you sew. Get some cool fabric and put them on the drums. You do have to take the hardware off and put it back on. Help your young drummer with this tedious task, it will be good memories. Hey you can clean and relube all screws and pivots with white lithium grease while you are at it.