That statement "Leave OSX alone - it's designed to take care of itself" is, of course, dead wrong! Toyotas are one of the most reliable brands of cars ever made, but they still need to be taking care of. Same is true for Macs. There are a number of things you can use (and do on your own) to keep your Mac "lean, mean, and clean". I will mention some, along with another fact about your machine. I'm sure others will have suggestions.
First, I also own a Mac Mini, but it is a late 2012 model. Both your machine and mine come with a slow, 1 TB 5400 rpm drive.. By "slow" I mean that it spins at 5400 rpm. To keep such a slow drive at peak performance requires disk cleanup/maintenance/repairs, from a software perspective. Myself, even doing all that I do (I will mention them below), the machine was still slow. And that was even when I was using a much faster browser, Google Chrome, than Safari (I rarely use Safari, as it is just too slow). So, after 4 months of "suffering", I replaced that internal drive with a fast Samsung 840 Pro 256 gig SSD, and the performance improvement was dramatic (I never needed 1 TB of space anyway, as I have (now had) a couple of 1 TB external drives I was using for backups and storage). The installation was not difficult at all, and I am so glad I did it. The internal 1 TB drive went inside a nice, slim Orico external enclosure, and I was using that drive for backups and storage. That setup worked out well (I have since move on to an all "SSD" environment, where my two external drives are now Samsung 850 Pro 512 gig SSDs).
Secondly, you can actually do a good amount of disk cleanup on your own. What I do for that is 1) always remove the prior version of an application I have been storing after an upgrade comes out, and 2) permanently remove deleted EMails. I use Outlook 2016 as my EMail client, and there is a simple keyboard combination to accomplish that. I do not know what the process is for other EMail programs, but I would think there would be a way (maybe someone can post how to do this with various EMail programs, like Apple's Mail, and Thunderbird, for example). Also, if I want to remove an application form my machine that I no longer want to use, just dragging it to the trash does not remove everything. Instead, I use the excellent freeware program AppCleaner for that, available from here:
https://freemacsoft.net/appcleaner/
It works real well to get rid of just about all the "stuff" associated with an application.
I am performing the permanent deletion of EMails a number of times each day (as expected), and the removal of prior versions of apps I am still using as often as needed.
Third, beyond that, there are a number of excellent products available (both free and commercial) that can help with the disk cleanup/maintenance/repair tasks. The two I use are the excellent freeware program Onyx, and the excellent commercial product TechTool Pro. Both of them have been around for a long, long time, are solid performers, and have excellent reviews. Here are links for each program:
Onyx:
https://www.titanium-software.fr/en/onyx.html
TechTool Pro:
https://www.micromat.com/products/techtool-pro
For Onyx, as you can see, there are different versions for each OS. Make sure you get the one for Sierra.
For TechTool Pro, besides its "common" features applicable to any type of disk (HDD or SSD), for HDDs, there are the Volume and File Optimization routines (they are not applicable, nor cannot be used, for SSDs). I remember when I still had the 1 TB drive inside my Mac Mini that such routines helped with performance. "Supposedly" the newer flavors of the Mac OS take care of that, but I never believed it. It's the same with Permissions Repair (available in both of those products, and applicable to SSDs also). I do it with Onyx, and it always finds permissions that need Repair (more so on my mid 2013 13" MacBook Air than on my Mac Mini).
I go through the process of using Onyx, TechTool Pro, and SuperDuper! (for my backups) once a week, typically on Saturdays, for both of my machines. I can tell you for a fact that I rarely, if ever, have issues with either of my machines. They are "lean, mean, and clean".
A couple of other things:
1. Disk Utility is "OK" for disk maintenance/repairs, but it is not as complete as TechTool Pro is. And it lacks a number of useful features which both Onyx and TechTool Pro have.
2. If you have any third party software (like Quicken, Office 2011/2016, etc.), do you have the latest version that is compatible with Sierra?
3. You are actually 3 versions behind for Sierra. Version 10.12.6 came out about 3 weeks ago, and you can get the Combo Updater from here:
https://support.apple.com/kb/DL1931?locale=en_US
It's always best to have the latest version of the Mac OS (and for that matter, any software that you have).
Last, are you making backups to an external device? That is
absolutely critical!! If so, what software are you using for that? Time Machine is OK, but in my estimation, a program like SuperDuper! or Carbon Copy Cloner is better, as each of them make
bootable backups/clones, and recovery is a lot cleaner and simpler with either of them. As I mentioned above, I use SuperDuper!, and of course I would not be without it!
