Hi arc1963,
I just saw this, and I would be happy to respond. I will say first that my disk cleanup chores actually happen just about everyday. That is, I am constantly deleting unneeded EMails (not permanently; see below), along with unneeded files/documents, etc. So, by the time I start my processing on Saturday, I am already in "decent to good" shape regarding further maintenance tasks. The other thing is that I have TechTool Pro's eDrive already setup on both of my machines. As you'll see, that is important. So, here goes.
First, I make sure nothing else is running prior to starting. That is, only the desktop is "active", nothing else.
Secondly, I use Outlook for my EMail needs, and even though I delete EMails that I no longer need, they do not get permanently removed from the Microsoft Identity file that contains my EMail database. So, the first thing I do is to launch Outlook, but also hold down the Option key. This brings up a dialogue that will re-build that database. Once that happens, a new Identify file is built, and the old one is renamed. I then launch Outlook again to make sure everything is good with the new Identity file (and as expected, it is). I then delete the old/renamed Identify folder.
Third, I launch Onyx, and except for "Erase Disk" (I have the El Capitan version of Onyx), I perform all the Maintenance and Cleaning tasks that Onyx has. Also, when I Repair Permissions (the version of Disk Utility in El Capitan no longer has that feature), I usually have to run it at least twice. Even when I had prior versions of the Mac OS, I still used the Repair Permissions feature in Onyx.
Next, I launch TechTool Pro, but given that some of the tasks it offers need to be done "externally", I then select the "Restart eDrive" option. This basically restarts my machine from the "isolated" eDrive partition on my SSD. From there, I first perform all of the Tests offered by TechTool Pro (I do not start with Check Computer (and in fact I do not run that at all), but run each of the tests separately). The order I perform the tests in is: 1) Memory Test, 2) SMART Check, 3) Video Memory, 4) Sensors Test, 5) Fans Test, 6) (for my MacBook Air) Battery Check, 7) Surface Scan, 8) Volume Structures, and 9) File Structures. The Surface Scan takes the longest, depending on the size of the partition you are scanning.
Next, under the Tools that TechTool Pro offers, I first run Volume Rebuild, and then File Optimization. If you have a "standard" HDD (non-Fusion), then after running Volume Rebuild, you should run Volume Optimization first, and then File Optimization. I used to do that when I had such drives, but with SSDs, Volume Optimization is no longer applicable. (I don't know about so-called Fusion Drives. You'll need to see what Micromat says about that).
Finally, I re-boot each machine from the primary/normal partition, quit TechTool Pro, and then run SuperDuper! for my two backups for each machine to two, separate external devices.
Please excuse my detailed explanation, but there are certain things that needed to be made clear. Also, this does take some time to complete, so I am doing other, non-computer chores while this is going on.