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My Mac Mini is the A1103 PowerPC1.42 GHz512 MB DDR SDRAM80 GB HDDRunning OS-X 10.3.9 I do not yet possess the DVI to VGA adaptor and I want to be sure to get the correct one. I think that it might be a 24 Pin Male to 15 Pin female for the monitor. But, I am not sure if it should be +1 or +5

Your mac Mini has a DVI port for the display connections. Here’s one possibility: DVI to VGA Cable Adapter - M/F Apple jumped around a bit after that, the Early 2009 went to the dual port offerings Mini-DVI port & MiniDisplayPort. The Mid 2010 then jumped to the Mini DisplayPort & HDMI. Then the Mid 2011 jumped to Thunderbolt and HDMI.