Monitor For 2012 Mini

Just bought an LG monitor that need 1920×1200 resolution. My Mac Mini only goes as high as 1280×800. Only two resolutions to choose from and the other one is even lower. Needless to say my new monitor doesn't look good. I'm using a DVI connection into my thunderbolt port. If I bought an HDMI cable (monitor didn't come with one) would the monitor then be capable to show at a lower resolution and look good?

I had a Samsung 24 inch that I used the HDMI to HDMI port. Video looked excellent but the text was a blurry and jagged so I sent it back and got this one. Now I have even bigger problems with the LG. So instead of rushing to send the LG back I'm trying to see if it's salvageable. Thanks.