Is this a good computer to play games with (specs)?

I'm thinking of buying a PC that has roughly these specs:
Windows 7
3GB RAM
320GB HDD
Video card: Nvidia GeForce 8800 GT or ATI Radeon 4600 HD
Processor: Intel Core i3/i5/i7 or AMD Phenom X2/X3/X4

How good is this PC for gaming? Will it be able to play games like Skyrim and Battlefield without lag? Can you tell me a better configuration?

Added (1). Ok so I found something a bit more specific and I'm asking the same thing: Will it be able to play next-gen games like The Elder Scrolls and Battlefield without any problems on at least medium settings?

AMD Phenom X4 955 3.2GHz
Windows 7 Home Premium 64-bit
500GB DDR3 HDD
ATI Radeon 68500 1gb PCI-E Graphics Card With HDMI
4GB DDR3 RAM

Lenovo Thinkvision L1951p 19 Inch LCD Monitor
Max Resolution 1440x900

I would want something with at least 4GB of RAM. But it's good that is has a Core i3/i5/i7 processor.

I hope I've helped!
If you have anymore questions please let me know by adding to this question, or posting a new one. Thanks!

** Looks pretty solid to me, hope it all works out

Thats kinda similar to mine. I have COD4 which runs pretty smoothly, but I'm unsure about Battlefield. Just look up the specs for battlefield on google, you should find it there!

Thats ok, but i would suggest a xbox for you http://www.thevideogameworld.co.uk/ good site for games. If your interested?