A big question that I see is whether or not a cable was advertised. At the same time, I've never bought a video card that had cables with it. The cables either came with the monitor itself, or were left for me to buy separately. If both your monitor and the video card are capable of DVI, I'd buy a DVI cable and use that instead of running things through adapters.
VGA is an analog signal, certain elements of the image will not be as sharp as a digital signal like DVI. I would not recommend using a vga cable when your monitor supports DVI, however you might have to buy one online, some places(such as radioshack) will charge outrageous prices for them. You can get one for around $10 shipped on newegg.
I have only heard of ONE videocard that came with an HDMI (atomic? toxic?). None that came with DVI. Some come with a pigtail s-video-to-component video converters. But that is all I have ever seen. Usually it is the monitor that comes with cables.
As for the cables, in the Audio/video world, an analog component video cable will only go up to 1080i, and HDMI/DVI digital is required for higher resolutions. I am not sure what that means in terms of VGA.
While HDMI does also carry the surround sound audio signal, I am almost 100% sure that sound will not come out of the HDMI slot on your graphics card. I believe the HDMI connection would be used more as a display option for an HDTV instead of a computer monitor.
Depending on your amp/reciever and speaker setup. You can use optical/coax cable to get the same quality sound as HDMI. And use DVI to get same video quality as HDMI. HDMI just makes everything easier for home theater because you only need to worry about 1 cable. (Coord from Blu-Ray to Amp/Reciever, Coord from Amp to TV) and that's it.