Looks like the integrated graphics of your computer only support VGA out. And yes the blue is the monitor out, VGA port. VGA is the older connection standard most commonly in use now, it sends an analog signal as opposed to a digital signal that is used by the newer standards.
This means just about all of the older monitors and most newer monitors can be used with this desktop as-is. If you want to be able to use DVI or HDMI which are higher resolution and digital ports then you'll have to consider getting a graphics card.
My suggestion for a really good and lower priced monitor would be something like this:
LG 22MP55HQ-P Black 22" 5ms HDMI Widescreen LED Backlight LCD Monitor, IPS panel ~$120
It's a 1080p IPS monitor. 1080p being it's resolution, 1920x1080 for 1080p or 1080pixels. And IPS being the technology it uses for displaying, In-Plane Switching, which has some of the best color reproduction and viewing angles.
If you really don't care for anything higher end then you could get something like this even for much cheaper:
HP Compaq LE1711 17" LCD Monitor - 1280x1024, 1000:1 Native, 5ms, 60Hz, VGA $50