1920x1080 the same as 1080p ?

It's the same thing, cables are mostly the same.
1080p just means 1080 lines vertical & progressive, in BluRay & Full HD specs it is 1920x1080.

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Almost but not...

1080P means 1920x1080 Progressive Scan. Which means all 1920x1080 pixels are updated in a single pass(Odd & Even Lines).

1080i means Interlace Scan. Which means odd and even lines(horizontal lines) of the 1920x1080 are updated alternately. The effective scan rate is 30HZ.

1080P and 1080I have the same 1920x1080 pixels. The 1080P has better quality as the entire screen is updated at 60HZ. The 1080i is updated at half the rate.

1920x1080 defines the pixel matrix of the screen (i.e. 1920 vertical pixels and 1080 horizontal pixels).

HDMI cables are rated base on its category or compliance to HDMI specifications. The latest HDMI specification is HDMI 1.3. If you want the best performance cable check for HDMI 1.3 rating on its box.

Below is the path for HDMI information and it includes HDMI cable rating and capability.

http://en.wikipedia.org/wiki/HDMI

As i stated HDMI cables are not the same. HDMI cables are rated base on its compliance to HDMI specifications. Right now you will be fine with HDMI 1.3. With the 3D HDTV due to come out mid or Q3 this year.... HDMI 1.4 will be required.

HDMI 1.3 cable will provide you with the best cable bandwidth for your PC or HDTV. It can support 1080P or higher.

Higher desktop resolution (i.e. 1080P) is always better. The best setup is run your LCD display to its native resolution. It provides the highest display quality base on the capability of the LCD display. Going 1080P will provide you with higher desktop space in your display to work with.

Game resolution is dependent on many factors
1) Native resolution of your LCD display(i.e. pixel matrix size, refresh rate)
2) Your video card's capability
3) Your CPU
4) Your game settings ( Game resolution, quality settings AA etc)

Your hardware is pretty good. You should be able to play games at high resolution with varying quality settings.

Below is the latest graphics benchmark that scale with cost.

http://www.tomshardware.com/reviews/best-graphics-card,...