Ok, some questions?

1. What kind of budget would you want?

2. Whats the native resolution of that TV, 1920 by 1080 is my assumption.

3. What considerations for power usage, noise etc are you going to make? Do you want ultra quiet, quiet or medium?

4. Is this your main gaming PC?

5. What kinds of games do you want to play on it?

Without some extra info I would suggest the Saphire with Vapour cooling as a power efficient, lower noise option for you.

Saphire HD 5770 $174 *mid range*

http://www.newegg.com/Product/Product.aspx?Item=N82E16814102868

Or if you're on a lower budget/want something to burn less power then:

HIS 5670 $99 *low power but still good performance*

http://www.newegg.com/Product/Product.aspx?Item=N82E16814161319

Or if you're building an uber:

An HD 5850 which comes with a 600W Thermaltake PSU for $299

http://www.newegg.com/Product/Product.aspx?Item=N82E16814102857

Now personally I would take the 5850 combo because if you're building from scratch then you need a PSU as well and that much more performance for only a few dollars more is incredible.

(All these cards either come with an HDMI port or DVI -> HDMI adapter which can do sound as well.

Edit: crossed out.

For a 1080p TV, your best bet will be a Radeon 4890. Pretty much all of them include either native HDMI or a DVI-to-HDMI adapter, but you should check to make sure anyway. Otherwise, as I said in the OP, all 4890 brands are pretty much the same; just get the cheapest one on Newegg.

Also, thanks for the comments, everyone!

Alright thanks,  I was actually leaning towards the "More Power" Box you have listed since budget isnt really an issue. 

Would that TV be fine or would you reccommend a different monitor??  

The Radeon 4890 has high idle power consumption and load power consumption. Its also far less efficient at the latest Direct X 11 games. I've seen upwards of 20% improvement over the DX10 path for certain games.

http://www.anandtech.com/video/showdoc.aspx?i=3658&p=7

http://www.pcgameshardware.com/aid,700050/Dirt-2-benchmarks-DX-9-vs-DX-11-Update-Radeon-HD-5970-results/Practice/.

http://www.pcgameshardware.com/screenshots/original/2009/11/Stalker-CoP-DX10-vs-DX11.png

That's all three DX11 games. First one has the cards about where I would expect from non-DX11 games, second has a large drop for DX11 and third a large rise. I wouldn't call that a win. Games developed entirely with DX11 from the start may well show a clear lead but there's few DX10-designed games 4 years after its release so it doesn't really matter.

The 4850 and 4890 offer better price/performance than 5750/5770. Conversely, the 5-series have much lower power consumption as you say. So choose which one of those you care most about.

Your TV should be fine. Heck, I run my PC on a 720p HDTV (at native resolution, of course) and everything looks wonderful.

Also, re the 4XXX vs. 5XXX series debate: Power consumption isn't an issue for most people, so I usually recommend the 4XXX series. If you want a "greener" card and don't mind paying a bit extra for it, though, there's nothing wrong with the 5XXX cards.

Im talking performance/watt for both idle and load conditions combined with performance. You can very well pay for less performance outright but still pay less overall for that performance with the 5770 because its got significantly lower idle and load power useage. In addition to this you can get away with a much cheaper PSU at the same time. Factoring everything in the 5770 is cheaper for the performance to run and its cheaper to build a system around that card. For a system which is just being upgraded it may be a different story however.

Im not saying that you're incorrect but that theres a bigger story to be told than outright performance for the dollar spent.

In addition to this the current DX11 hardware still has performance improvements from drivers to be expected whereas the older has been pretty much tapped for all easy gains. Furthermore developers have the option of either increasing image quality or performance when they implement DX11, this is something that older hardware can never take advantage of.

At the present time, I wouldn't worry about DX11. There's no games on the horizon that require it, and only three out right now that even use it. Save the DX11 concerns for two years from now when you upgrade your graphics card.

No game will require it for a long time but they will soon drop DX9 support and focus on the DX10+ codepath. Pretty much every feature in DX11 can be emulated by DX10 hardware aside from tessellation. However emulated support for more advanced shaders etc will be slower than native support. So by the end of this year there should be a clear lead for the 5750 against the 4850 and the 5770 against the 4870. In addition to this the other abilities of the GPU are more useful, like for example accelerating encoding or GPGPU type tasks with Shader Model 5.

There's really no evidence at this time to support anything that you said. Again, at the moment there's only three games that support DX11, and the only notable ones coming in the future with announced support are Aliens v. Predator, Battlefield Bad Company 2, Crysis 2, and a couple of MMOs. And those will display just fine on a DX10 card.

As always, buying with "future-proofing" in mind is stupid. Just get a DX11 card in two years when more than a handful of games can utilize it and you'll need to upgrade anyway.