HTPC - Antec ISK 300-150

Hey there chriscalderonh, welcome to the HTPC crowd here at Tom's.

Excellent build you've got going there. I hope you keep us posted on the progress. For Christmas, my brother got me the ISK 310-150 case but I haven't started my project yet. Anyways, about your questions:

The integrated video on your Clarkdale processor will do everything you need. A discreet card is only needed if you want to game. That said, I would recommend against adding a separate video card since it will only add heat/noise to your setup without adding much to your HTPC experience. Even if your card is passive, the PSU in your ISK will be working harder and have its fan turned up to compensate for the extra heat generated.

Now that I've given you my recommendation, here are the trade-offs for not getting a discreet video card:

The HD5570 has the muscle to perform Vector Adaptive (VA) post processing while the integrated cannot.
The HD5570 can properly output 23.976 fps to match the framerate of film while the intel integrated cannot (it's not that the integrated is too weak, it's because intel made an error in the hardware... AMD chipsets do not have this limitation).

The first point is only a problem if you watch a lot of high contrast interlaced content (results in jaggies on, for example, the lines of a football field when the camera pans). Truth be told, you would never notice unless someone gave you a specific interlaced film and held a magnifying glass to your TV screen.
The second point is something that videophiles will cry about. Most likely your will be running at your 1080p at 60Hz. If you play a film on your TV, about every 4 minutes there might be a slight judder due to the mismatch in frequency if it happens during a panning fast motion shot. Again, I would wager that you would never notice it unless a videophile pointed it out to you.

Hope this helps.