You can use HDMI cable with HP w2207h directly,No need for other cable. but please follow these step.
1.Find LCD tv to set up first step.
2.Connect HDMI cable to LCD TV(i use Samsung) and adjust to HDMI source.
3.Open Mac mini.
4.Open system preference.
5.Click "display" you will see that the primary setting is :1680*1050 that HP monitor did not support.
6.Unplug HDMI cable from LCDtv (no need to shut down) and plug into HP w2207h.
7.the screen still blinking, it is ok.
8.On HP monitor, Push down button "Select" and "+" and the same time and hold it.
9.Use mouse or down button on keyboard to choose screen resolution to be "1600*900"
10. Then the screen will not blinking and you can use your lovely HP w2207h
if you want a high resolution on screen.
1.Buy new LED monitor that support 1680*1050 resolution.
2.Buy Mini displayport to DVI for digital signal Mini>DVI>HDMI.
Enjoy your MAC. because i am new Mac user with my MAC mini