Apple - Dual screen with new Mac Mini
The general answer is your Mac Mini 2014 has two Thunderbolt 2 ports so your best bet is to drive one monitor from HDMI and the other from Thunderbolt so that you have another Thunderbolt port free for storage or networking.
Out of the box, fully supported by Apple is either two displays via Thunderbolt (and they can chain if one of the display is actually Thunderbolt and not DP or another adapter) or one display via Thunderbolt and the other via HDMI.
See http://support.apple.com/en-us/HT5219#18
MacBook Pro (Retina, Mid 2012), MacBook Pro (Retina, 13-inch, Late 2012), and Mac Mini (Late 2012 and later) computers can use an HDMI-compatible device on it's HDMI port while using one Thunderbolt display, or they can use two Thunderbolt displays.
If you can't or don't want to use Thunderbolt or HDMI, you could avail yourself of USB adapters. The part you listed looks like it will connect to a Thunderbolt port and end that chain and be seen by OS X as one display no matter which of the older ports you connect to one (or more) displays.
You connect two monitors to a Mac Mini via two separate ports; one monitor for one port.
It sounds like with both your monitors you'd like to connect via VGA. So then you'd need:
- Thunderbolt Mini display port to VGA adapter.
- HDMI to VGA adapter.