It looks like Hereford XL needs almost 16 GB by itself, and the latest Mac OS wants almos 1/3 of its memory free, else it refuses to run audio drivers. So I'd look for 32 GB RAM.
To compare CPU capacity between processors, this web site is useful:
https://www.cpubenchmark.net/CPU_mega_page.html
You could start with your current Mac Mini's CPU model, and compare CPU Mark and Thread Mark numbers against the ones you're considering buying, but given its age, newer processors should usually be several times faster.
I can make the definite statement that my previous i9-9900 could handled Hereford XL up through Hauptwerk 6 Higher audio engine quality, so that could help decide what's enough CPU capacity.
The Minis released in 2014 ranged from i5-4260U to i7-4578U, and the i9-9900 is more recent.
The corresponding CPU Mark ratings are: 2344, 3031, and 16763.
The Thread Mark ratings are 1480, 1927, and 2854.
If you can buy something with at least 17000 CPU Mark and 3000 Thread Mark, it's a sure thing for running Hereford XL on HW 7.
This site has specs for past Mac models:
https://everymac.com/systems/apple/inde ... espec.html
If you find a used one to buy with at least 32 GB, check the CPU ratings to make sure it's rated around 17000 CPU Mark and 3000 Thread Mark or more, and make sure it supports upgrading to a Mac OS that Hauptwerk, iLok, Apple, and your audio and MIDI interfaces support.
The highest 2018 Mac Mini CPU was an i7-8700B at 12097 CPU Mark and 2759 Thread Mark. It might be enough -- others here might run Hereford XL on that.
Certainly an M1 is more than enough CPU, but a 16 GB machine won't load Hereford XL at 24 bits, so you'd still need more memory on an M1 based Mac.