A few thoughts on the Mini... as was posted, be wary of the 2014 Mini, the RAM cannot be upgraded (although you can add a SSD pretty easily). The base 2014 1.4ghz Mini really should be avoided entirely, the 2014 2.8ghz i5 and 3.0ghz i7 might be suitable, but it could be hard to find these with 16gb RAM.
The 2012 quad-core Mini's are worth looking for, there was a 2.3ghz and 2.6ghz version that are pretty close in terms of speed. RAM was designed to be user-upgradeable and is very simple. SSD can be added/upgraded but it gets into relatively complicated surgery. They can only accept a maximum of 16gb of RAM, but CPU performance is about the same as the entry-level i3 2018 Mini. These 2012 quads are actually about 50% faster than the top-spec 2014 Mini. The 2018 has a number of other advantages however.
For your budget, it sounds like you could afford a used 2018 Mini, which would arguably be the best choice in terms of support and compatibility with new software. RAM was not intended to be user-upgradeable, but it is possible and many people get the base 8gb model and do their own upgrades (up to 64gb max). But be aware of what you are buying, Apple's official policy is that user-upgraded RAM voids the warranty (although they may or may not enforce this).
I have seen several enthusiastic reviews of the 2018 Mini from people involved in music production. Some even suggested they were the perfect target for the 2018 Mini, since the main complaint has been the graphics chip, which doesn't matter with audio software.
I have been running Logic Pro going back to my 2011 MacBook Air which only had 4gb RAM and a 256gb SSD. It actually worked fine for my own needs. It runs even better on my 2013 MacBook Air with 8gb RAM - but much better still on my 2012 quad Mini with 16gb. My needs are pretty basic though, live recording with 8 tracks and some basic plug-ins like reverb & EQ. Looking forward to trying it on my new 2018 Mini, but I'm still in the process of setting that up.
For your budget you might also afford a refurbished 2018 Mini (not quite sure of the pricing in your country), which has the same warranty as new. Just got a 2018 refurb myself, and nobody would be able to tell it isn't brand new. You need to check the refurb store frequently, there are lots available but they sell very quickly and then there are none for days. Be prepared to buy immediately if you find one that you like. Took me a little over a month of constant checking to score the exact model I was looking for.
Save up to 15% on a refurbished Mac. Tested and certified by Apple including a 1-year warranty. Free delivery and returns.
www.apple.com