Mac Mini

No, you will need an external monitor for the new 2020 Mac Mini.

see > Use your iMac as a display with target display mode - Apple Support

You can use a supported iMac models as a display, but only with a 2019 or earlier model Mac.

If your old 27" iMac it is a Late 2009 thru 2014 model then it does support Target Display Mode. The problem is, the new 2020 Mac's including the 2010 Mac Mini does not.

If it's a 2009 or 2010 27" iMac, it will work as a display for a 2020 Mac, despite what Apple says. You will need a USB-C to Mini DisplayPort cable.

mophie USB-C Cable with Mini DisplayPort Connector - Apple

Not really, because I personally prefer to run 2 smaller 21.5" and 24" displays on both of my Mac Mini's.

(I have 2 LG 21.5" displays on one of my Mac Mini's and 2 Samsung 24" displays on the other)

To be honest, I haven't though much about going back to a single larger Display.

(If I did, I would start by looking at and comparing some 27" to 32" displays)

For some good ideas,

see > https://9to5mac.com/2020/10/27/best-4k-usb-c-displays-for-macbook-and-macbook-pro/

and > https://www.digitaltrends.com/computing/best-monitors-for-mac-mini/

or > https://www.rtings.com/monitor/reviews/best/mac-mini

This may help

https://www.lifewire.com/use-imac-as-monitor-with-target-display-mode-2260906