Graphics Card for PCI Express 2.0 x16

clutchc

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I'm not comfortable recommending a powerful card with that PSU. It is one I'm not familiar with and one I believe may be of poor quality. But the framerate you desire will depend on the resolution of your monitor. The greater the resolution, the faster the card needs to be to render the pixels/texels at 60 FPS. So the first thing we need is the rez of your monitor. next would be your price limit.
 

clutchc

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That no-name PSU is worry-some. It is ranked in the last tier of quality, tier 5... the not recommended tier.
http://www.eggxpert.com/forums/thread/323050.aspx

On top of that, it doesn't even have a single PCIe 6 pin power cable for a graphics card... and only has a 25A (+12V) rail. Therefore, I will hesitantly recommend this card as the max you should use. It will get all its power from the PCIe X16 slot itself.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814121710
And it is about the fastest card you can get that doesn't require a separate power cable.

It should provide smooth frame rates at high settings with your HDTV's 720p resolution. If you upgrade to a 1080p display some day, you will want to also upgrade your PSU to a better quality one so you can buy a faster card. In fact, I recommend you upgrade to a better quality PSU anyway.
 

clutchc

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Yes it will work fine. PCIe is a backward compatible protocol. The card will simply run at 2.0 speeds instead of 3.0 speeds. But that is a moot point, because that card (like most) could never saturate the bandwidth of 2.0 anyway.

PCIe 2.0 has a speed of 500 MB/s in each direction per lane
PCIe 3.0 has a speed of 985 MB/s in each direction per lane

Your graphic card slot has 16 lanes.