Wow, there's a lot of testosterone pumping over this answer.
OP, the first thing I would put in perspective is that you have placed a price. $600 for a toy. That's a very generous donation
. As a parent, your focus is on education and their personal improvement, with fun where it can be had.
If your teenager wants more, let them earn it. It's much like their first car - you want it reliable and able to get them to work and home. Let them add the extras for fun.
That said, let's put your donation to good educational use, and let the teen build the extras:
first, start with a desktop. This is still the cheapest, most powerful option. My 5-year-old desktop still tromps my 1-year-old notebook. My notebook cost over $1.2k and can eat its 8-cell battery in under 20 minutes if I push on it.
I would build my donation based on what it would take to build a basic machine, with a bit extra just to keep it reliable. Hop on newegg and start adding the following to your cart:
-Motherboard. Find an Intel board. They are typically rock solid and sometimes even high end.
-Processor (an i3 processor will be fine for most school tasks unless they are have expressed interest in graphics, software, or engineering)
-RAM (I've been out of the game on this, but i assume 8GB is fine)
-Operating System and Microsoft Office. Buy this through the school at a HEFTY discount.
-Hard drive. I get by with 500GB just fine, but it's your call. New Dells ship with 1TB. SSD drives are nice to haves.
-Really good budget cases can be had for $50 - $80. Some of the ones I bought were more of a joy than my big spendy cases.
-If the motherboard doesn't have on-board video, then look for a simple ATI or nVidia PCI 3.0 video card. HIS, eVGA, XFX, ATI, MSI are excellent choices. A good budget brand is Sapphire.
-Power Supply (you can use the calculator on newegg.com
to figure out how big, but you may want to keep ~400W as a minimum). A good choice is Antec as a baseline.
Also if you have any tech savvy-ness (or a friend), I recommend having the teen put it together. It is an excellent learning experience and can open up a lot of great summer jobs that pay handsomely.
I was able to create a reliable machine that cost $533 (before software) on Newegg just now. The teen would need to put more money into the power supply and get a dedicated video card, possibly more CPU, but otherwise I've provided them with a healthy amount of the computer.