What are the advantages of the mac mini's hdmi output?
If you keep your machine plugged into one display, there won't be much of any 'fiddling'. And even if you switch, 10.7 actually is supposed to help with switching displays (as in, if you go from a LCD monitor to a TV). 

Another advantage is that the machine was just updated, so depending on how much you are willing to pay, you are going to get a more powerful machine than what you have now. 

As you said, you will also have HDMI out, which will contain audio as well. 

Finally, you will need to purchase a display, mouse, and keyboard if you don't already have one.