Mac mini late 2014, how do I get maximum 2550 x 1660 resolution on external screen. What cables and ports do I use?

What display do you have?

If its a Thunderbolt display, connect it to one of the Thunderbolt ports.

Any other type will use a Mini DisplayPort cable or adapter from one of the Thunderbolt ports. Do not use the Mac mini's HDMI port for 2560 X 1600.

@steveKJ: On the 2014 Mac mini, you would need to use either of the Thunderbolt 2/mini-DisplayPort ports to achieve this resolution.

@Malcolm J. Rayfield: Sorry Malcolm, I replied to your tread by mistake.

Hi Steve, go to the Displays preferences, hold the Alt (option) key and then select the Scaled button.

The HDMI port can't support resolutions greater than 1080p at 60Hz.

Mac mini (Late 2014) - Technical Specifications

"HDMI video output

Support for 1080p resolution at up to 60Hz

Support for 3840-by-2160 resolution at 30Hz

Support for 4096-by-2160 resolution at 24Hz"

"why is it best NOT to use HDMI.."

Because the original incarnation of HDMI was for use with HDTVs (1920 x 1080 aka 1080i), not computer monitors. MiniDisplayPort was designed for use with computer monitors. Later versions of HDMI have higher resolution capability.

See: https://en.wikipedia.org/wiki/HDMI