Its not a bad spec for the price, and if you have never had a PC capable of playing games before then you will certainly enjoy been able to play the latest titles, compared to a 360 / PS3 your going to notice a huge difference.
The 6670 graphics card is what i could call an entry level graphics card for gaming, it will play the latest games, just not in the highest detail / frame rate. However that's the great thing about a PC, you can just upgrade the graphics card at a later date if you want more power.
Other than that you have plenty of ram (double what i have!) a good processor, lots of storage space and a pretty nice looking case too.
For the price you paid i think you got a good deal there.
Maybe you can post a review up for us with some photos once you have had a good play about with it? would be interested to here what you think of it as a first gaming PC.