When a game talks about minimum requirements, it means what it takes to run the game, graphics quality and framerate be damned. Minimum, indeed. Minimum playing experience, that is.
Recommended usually talks about what it takes to run the game on low graphics quality but still run at 30+ frames per second. The game is playable, but far from ideal.
In other words, take the "recommended" hardware and pile on another $100-$200 worth of game-processing hardware muscle before the game will look really, really good.
Instead of going by those benchmark sites and what's on the box, learn what hardware numbers are good or not.
CPU jargon:
Dual-core is alright for the less intense games from 5 years ago, especially since they're processing more efficiently than ever. Plus, a 3+GHz dual-core is relatively cheap these days.
Quad-core is going to work for you no matter what, and the high-speed 3.0GHz versions are relatively cheap.
RAM:
6GB minimum for the new stuff. 8GB is better. There are a bunch of different speeds, but it's a pretty good chance you'll be getting the DDR3 1333MHz. Take a close look at the motherboard specs to know what to get.
Video card shtick:
This is where things can get hairy. I guess the easiest way to tell if a video card is strong is to either know the video card series OR look at how much dedicated memory there is on the card. 1GB video memory is really good and will play anything in HD. You can get a Radeon 6850 or Geforce 550 for $150 or so, a really good value.
If you want to cheat, get two identical, less-powerful cards and put them into an array (Radeon Crossfire or GeForce SLI). As long as they have the HDMI ports on them, you're probably good to go.
The Accelerated Processing Unit (APU)
A relatively new thing is the APU, which is a CPU chip with an integrated graphics driver, putting the two techs into one little oh-so-convenient package. Intel chips have their own half-assed APUs, but the only real choice right now is the AMD A8 with a moderately-powerful graphics driver. This piece of technology is a godsend for beginner gamers and anybody not planning on doing heavy gaming (family PCs and home theater PCs).
Granted, I doubt it'll play the likes of Deus Ex: HR and other "graphics porn" games at anything over moderate settings, BUT it's an ideal place to start.
And I checked, an equivalent dedicated CPU+video card cost about $50 more than the APU.
Anyway, for the love of god, upgrade. I highly recommend you try to put together a list of components for a hypothetical moderate gaming rig, it's the best way I can think of to learn all the jargon and know what is or is not "powerful" by today's standards.
Word of warning: A moderately powerful PC is going to run you $700-$800, and the prices only get more painful from there. I hope you already have the HD monitor and the mouse+keyboard you want, too.