Compliant = doesn't horribly b0rk-b0rk when you install that version of DirectX.
DirectX 6.1 = basic triangle setup and rasterization, the most fundamental parts of 3D.
DirectX 7.0 = fixed function transform and lighting. GeForce 1 has this.
DirectX 8.0 = Pixel Shaders 1.1 and Vertex Shaders 1.1, IIRC, GF3+
DirectX 8.1 = Pixel Shaders 1.4 and Vertex Shaders 1.1, Radeon 8500+
DirectX 9.0 = Pixel Shaders 2.0 and Vertex Shaders 2.0, 9500+
A G550 is a DirectX 6.1 part with PORTIONS of a fixed-function transform and lighting pipeline, for HEADCASTING!!.... It's more like DirectX 6.5 than anything, but it's far from a DirectX 8 chip, it's just COMPLIANT.
Radeon 8500, for example, accelerates all of DirectX8.1 and below in hardware, and it's DirectX 9 *compliant*, which means it can let the software renderer do any DX9-specific stuff, if the game/app allows it.
As for TV viewing.... The only things that are even sort of relevant:
A good PCI bus. Intel preferred, AMD/Nvidia/SiS acceptable, Via/ALi no-go. It'll probably WORK on any of them, but probably not well.
A good overlay. My TNT2 had great overlay support. It's basically a really simple path for something to dump video straight to the DACs, without involving CPU processing, or tons of memory copies.
Any halfway decent non-integrated card with over 16MB of video RAM or so ought to be able to toss up a 1280x1024 or 1600x1200 video overlay. If you are getting jumpiness or stuttering when you full screen a video at 1600x1200, then the card is probably out of ram for the overlay to use, and it's falling back to simple blitting or even full-software video.
Getting even a bottom of the line 32MB or 64MB card will allow overlays at higher resolutions. Yesterday I created a 2560*1024 overlay surface on my 9800 128MB.... Possibly the first thing I've done where a 128MB card outperforms a 64MB one.
For 1600x1200, at 32bit color and at 85Hz or 100Hz refresh (flickering at high res is often your monitor's refresh rate crapping out, you need 60Hz to have it halfway watchable, and many people still get headaches off of video on a 60Hz CRT... You want at least 75 or 85Hz for a truly smooth picture).
In other words, that Radeon 9000 will be overkill if all you want is 2D and video. Getting good 2D sharpness is a bit harder to judge for you. You'll generally want to avoid the cheapest cards, as the board makers will cut down component quality first thing, when they're looking to have the cheapest card out there. If a Radeon 9000 is exactly what you want, try to get a Built By ATI (BBA, ATI brand) card, as they are fairly strict on card quality. Buying a Powercolor, for example, is 2D quality suicide. Those cards are really cheap, and it shows.