You neglected to add a video card, which is required to actually connect a monitor to the computer. If you want to play games on the computer at 1080p, you'll need to spend at least $150 on a video card.
He mentioned that he was going to be using an HP case, but in my experience, you frequently can't install standard ATX motherboards in them. Also, the PSUs that come with pre-built computers are usually garbage, capable of running only the hardware that was already in the computer and nothing more.
Personally, I think he's got somewhat unrealistic expectations of cost. He needs a minimum of $180-200 more in hardware over what he's already picked, probably another $50 on top of that for a case.
For the full $600 it should be possible to build a decent system.
Recent testing and articles (you can find them on Tom's) have shown that there is no longer any price point where Intel does not outperform AMD. Disclaimer: I'm not an Intel fanboy, in fact over the last few years I've built almost all AMD systems. I just don't know when I'd build another one.
Ok here's a build. There's nothing here I wouldn't buy myself, and some I have:
Western Digital Caviar Blue WD5000AAKX 500GB 7200 RPM SATA 6.0Gb/s 3.5" Internal Hard Drive -Bare Drive
$84.99 -$10.00 Instant $74.99
I've used a number of the WD Blue drives. Nothing remarkable, but they've been reasonably quiet, and performance is decent. Stay away from the slower "green" or LP drives.
HIS H675F1GD Radeon HD 6750 1GB 128-bit GDDR5 PCI Express 2.1 x16 HDCP Ready CrossFireX Support Video Card with Eyefinity
If you don't need an O/S, this is the first thing to increase, for better game performance. For the price though, this card should do pretty well. A HD7770 or HD6850 would be worthwhile improvements for another $30-$40.
Intel Core i3-2120 Sandy Bridge 3.3GHz LGA 1155 65W Dual-Core Desktop Processor Intel HD Graphics 2000 BX80623I32120
$124.99 -$10.00 Instant $114.99
Will match or beat any current AMD CPU in games.
Rosewill R218-P-BK Black SECC Steel ATX Mid Tower Computer Case
I've built in this case, and it's not bad for being a cheap case. The fan is quiet, and moves a decent amount of air.
ASRock H61M/U3S3 LGA 1155 Intel H61 HDMI SATA 6Gb/s USB 3.0 Micro ATX Intel Motherboard
$74.99 -$8.00 Instant $66.99
Has modern interfaces like USB 3.0 and SATA 6Gb/s. I trust ASRock for mobos far more than I trust MSI.
Antec EarthWatts Green EA-380D Green 380W Continuous power ATX12V v2.3 / EPS12V 80 PLUS BRONZE Certified Active PFC Power ...
Model #:EA-380D Green
$59.99 -$15.00 Instant $44.99
Has been my "goto" PSU in budget builds for years. Efficient, quiet, and reliable. There's a 430W Corsair available for a little less right now (if you play the rebate game and win), but this is a higher quality unit. The CM you listed in your last post, btw, is near junk; read the review of it at HardwareSecrets.
G.SKILL NS 4GB (2 x 2GB) 240-Pin DDR3 SDRAM DDR3 1333 (PC3 10600) Desktop Memory Model F3-10600CL9D-4GBNS
G.Skill has become my first choice for RAM because I've never had to return any; it just works.
Sony Optiarc 24X DVD Burner, Bulk Package Black SATA Model AD-7280S-0B - OEM
One optical drive is much like another. You'll spend another few $$ if you want Lightscribe.
Microsoft Windows 7 Home Premium SP1 64-bit - OEM
If you already have a [legal] copy of Windows, I'd add a chunk of this to the video card (HD7770 or HD6850) and perhaps a slightly nicer case.