Well, Intel HD4000 can max Portal 2 I heard. I really recommend getting parts and building a computer yourself though, since it will be even cheaper and really suit /your/ needs. If what you're looking at is decent performance, I'm affraid $600 is not enough though. For gaming, an i5 with 6-8 GB RAM and a dedicated GPU is recommended.

Playing minecraft on an intel hd 4000 at 1920x1080 gave me an average of 40 fps with a 3rd gen i7. If you got one of the computers you talked about at best buy, ask a worker if the desktop would support a gpu such as the gtx 650 and has the 6-pin power connector for it. Then buy a gtx 650 online (it's around 110 bucks), or a similar card, and throw it in there.

Like streetwalker said, you are much better off just building a cheap rig, and can easily make it around $500.
To play those games and many more, this is an example build:
CPU: almost any modern amd or intel (I have a media center with a $120 core i3 that runs anything I throw at it)
GPU: a 100-130 dollar card would easily run all those games and more
PSU: a 550-650W power supply would be more than enough if you are running a mid range gpu
RAM: 4 gigs is enough for playing games like that
Then you can find a cheap mobo that works with the cpu, gpu, and psu, get a hard drive and dvd drive, and a cheap case for about 30 bucks.  Again, this can all be built for around $500.  Gaming rigs that are prebuilt usually start at around 750 if they have a decent gpu in them.

the integrated GPU on the AMD processors blows away the Intel GPU's

Not surprising since AMD's IGPs are directly derivated from the Radeon HD discrete GPUs.

I honestly don't know. I'm not documented at all regarding AMD CPUs since I read they were crap so I looked at Intel for my own build. Someone could tell you more.

Quote from: ElementCoder on July 04, 2013, 01:23:35 pm

Well Intel HD are not even cards, they're just chips so they won't help you with gaming. Like Streetwalker said, the best you can do is gather parts and build it yourself.

that is not at all true. ivy bridge's hd4000 can handle his mentioned games, and haswell has improved on that performance again, with the high-end iris chips nearly doubling performance. yes, there are plenty of dedicated cards that are much better, but it is no longer true that intel's integrated graphics are "worthless" (and they're a particularly nice choice for linux/bsd/etc users)

as for putting together your own computer, that is definitely the best way to lower prices, but it takes a lot of patience and experience to find the right parts at good prices and make sure everything fits together properly in the end. that's not to say that you shouldn't try =)

I didn't mean to say they were worthless, I have a pc with only the HD4000 and it works like a charm indeed I just meant that if you're looking for some serious gaming you'd be better off with a dedicated card than with a chip.

I've been told a lot to build my own computer but I don't see any way it could lower costs so much that it would be worth doing.

Well for one you don't pay the branding of whatever manufacturer which built the computer. This doesn't make it insanely cheaper but sometimes you can fit slightly better hardware for about the same price when building your own comp. Plus it's much more suited to what you wanna do with it since you choose to privilege a part instead of another.