I have both the new 2018 Mac Mini and the LG 34WK95U 5K2K widescreen display. I can tell you that it has been nothing but problems. Worst first use experience for any Apple product I've ever had. The mini has sync/handshaking issues with this display and will often just stay blank when waking from sleep. The mini is awake and active since I can screen share into it. Sometimes removing the TB3 cable and reinserting will 'wake' the video display, but more often it won't. Reboots are hit and miss as to whether I will get any video display. I know the display is fine since I used it on another Mac and it works fine. Thought the mini was a lemon but then found MANY threads on Apple Support site referencing issues with external display problems and the new mini. Those problem mirror my own.
I have a support case escalated with Apple Support. They acknowledged the issue and Apple Engineering is aware and working on a fix. The hope is that it will make it into the 10.14.4 release. Essentially I have $3500 of gear that is not really usable. Returning the mini just leaves me with a $1500 display I can't use. Getting a replacement mini is unlikely to solve the problem. Have done EVERYTHING to solve this including wiping the internal drive, multiple OS reinstalls, installing 10.14.4 beta 3 (which has it's own issues with BridgeOS on the mini). None of it works.
So I would say stay away from this configuration until you get confirmation that Apple has fixed the issue.