The 'smallest' hi-def resolution is 720p. This equates to the resolution of 1280x720 pixels in the display properties (under Control Panel) for Windows XP/Vista.
The TV stations that broadcast in 720p are: ABC, Fox, ESPNHD

Other hi-def resoltion are 1080i and 1080p. Both are in 1,920x1,080 pixels.
Stations that broadcast in 1080i are CBS, NBC, PBS, DiscoveryHD Theater.

1080p source is usually from Blu-ray players, PlayStation 3 and Xbox 360.

One example of hi-def graphic card is VisionTek Radeon 3870X2 1GB Pcie Dual Dvi HDtv (from Amazon $274 + shipping).

The other things that you also need to factor in are the CPU (as this would help during encoding and decoding process) and the monitor to display such hi-def content. Please note, if the broadcast content is copy protected, you needs to find graphic card that supports HDCP.
Source(s):
ATI Radeon™ HD 3800 Series - Overview
http://ati.amd.com/products/Radeonhd3800/index.html

Amazon - Radeon 3870X2 1GB Pcie Dual Dvi HDtv Out Sup 5.1 Sound
http://www.amazon.com/gp/product/B0012VJNF4

HDTV resolution explained
http://www.cnet.com/hdtv-resolution/

Wikipedia - High-bandwidth Digital Content Protection (HDCP)
http://en.wikipedia.org/wiki/High-bandwidth_Digital_Content_Protection

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