HDMI is a repackaging of DVI with support for audio. Encoding is the same, so a DVI to HDMI adapter is a passive component in all of this. Can you lose quality in the passive component? Yes, you could. Is it something to worry about? Likely not.
I do not believe that computers are going to HDMI. If this really is going to be a monitor for your computer and not something that doubles as a television, then I'd stick with DVI. It's what computers output now and it will be what computers output in the near and foreseeable future.
If you want the flexibility of using it as a television later, then sure, go with HDMI.
In either case, I don't think you can lose.