Jeez, someone just help this guy out....
Look, right now ATI is the better in my opinion, but first things first, you likely don't even have the power to use anything that's even been recommended yet.
If you want a card that well supports HDMI and won't break your budget, a Radeon 47xx/57xx series card would do just fine. You should shop for a power supply as well, you can probably pick up something with 2 Pci-E and enough amps to power those cards for under 100eu, just gotta shop around.
Also, there are sites that sell Psu's and Gpu's together, just the same as sites sell mobo's and cpu's together. My cousin just spent $1,200 on an HP Elite PC, totaly decked out, but...!!! 300watt power supply!! Barely enough power for the system, maybe a drop to spare.
So, I'm gonna go ahead and just keep this simple, and let you decide, and then you'll need to choose a source, where to buy. If you want more information, entirely unbaised, PM me.
I would shoot for a XFX Radeon HD 5770, and at least 500watt power supply (Pci-Express capable...although virtually all are) from PC Power & Cooling. If you cannot get from PC P&C, go for Thermaltake.
If for some reason you absolutely don't want an ATI card, I cannot recommend more than a GTS 250, from Nvidia. It will have dual DVI...perhaps there's a model with HDMI I'm not sure, but this won't stop you from using HDMI, as you already know.
The next card up in my opinion, considering price and what ATI is doing, would "have" to be a GTX 260 448 bit, 216 shader model. Anything less you're throwing money away, you could grab a Radeon HD 4870, or the highly optimized 4890 and OC the hell out of it, but I'm going to assume you want to install, and be done with it, power from the get go.
ATI= 5770, Nvidia= GTX 260 448bit 216s. Now the 5770 is more powerful than the Geforce, it's just that you don't need anything more from Nvidia, and their prices aren't friendly, however they may be when the GTX 470 and 480 drop, very soon.
If you can, wait a month, otherwise, I'd shoot for an ATI card. There's just so much to choose from, ranging from DX10.1 and DX11 gens, this creates separation from Nvidia and allows for a huge market of ATI cards (budget mostly) to be had very cheap. 550watt Psu should be plenty for what I've mentioned, it's mostly the amp-age that matters but any Pci-E Psu at 500w will be sufficient for what I've recommended, assuming you're not running an extreme system.
P.S. There are vendors that will sell you an video card, "and" a power supply, together, with great warranties. In fact if you decided to go with Nvidia, I'd say visit BFG's web page.
Forgive the length, it's a very broad topic. I can give you links and unbiased reasons for choosing Nvidia or AMD, via PM "ONLY", otherwise people will flip out and start arguing in the thread
GL