Need some advice/solutions on having 2 external displays set up

It is able to do so, I'm doing this exact thing right now. I've got two 1080p monitors connected, one via HDMI (to DVI), one via Thunderbolt (also to DVI) - works all fine :-)

You can indeed use both the HDMI and Thunderbolt ports to drive two separate monitors with a Mac Mini.

Any Mac with a Thunderbolt port can use any mini Displayport display, cable or adapter, so you're correct that the mDP to DVI adapter is what you need¹. If you have a display that requires dual-link DVI (typically only monitors with resolutions higher than 1920x1200), you'll need an active mDP to dual-link DVI adapter.

For the HDMI port, HDMI to DVI adapters are readily available (HDMI is essentially a superset of DVI with a different connector). Note that the HDMI port is limited to monitors with 1920x1200 or lower resolution.

_{¹ Note that the reverse is not true - Thunderbolt monitors can't be used with mDP equipped Macs.}