Cool. Yeah, I got the latest version of TechTool Pro also earlier today. Don't forget that after you upgrade to TechTool Pro V9.5.1, get rid of the "old" eDrive, and create a new one. Then, you'll be up to date with that also. Also, when you upgrade to the new Mac OS, you'll need to delete the eDrive again, and create a new one, which will be based on the newer Mac OS you plan to upgrade to.
Now, regarding your plan of attack, here are some suggestions/comments/assistance, etc (as you'll see, a lot of it is based on you choosing Yosemite to upgrade to):
1. You can actually use SuperDuper! in demo mode (note where it says "Download the free trial now"), and here is the company's site:
http://www.shirt-pocket.com/SuperDuper/SuperDuperDescription.html
Note that the latest version, V2.9.1, is compatible with OS 10.8 and above. When you use it in demo mode, it has just about all the functionality as in paid mode, but it runs "somewhat" slower (but still at a decent rate). I actually used it in demo mode for almost a year before I purchased it. As you can see, the paid version is available for $27.95. I have been using it for a long, long time, and I would not be without it. To repeat, when you launch the program, select your "system" to be copied/cloned, and then the destination external drive (maybe partition on your external drive), SuperDuper! will create a
bootable backup/clone. When it is done, you can restart your Mac
from that backup/clone, and it will be just like having another Mac. You can then run anything from that backup, like you would on your Mac. That's the beauty of it.
2. The first thing you should do is download the Mac OS you want from the App Store. So, if it's Yosemite, that should be V10.10.5, the last one. After you download it, a file entitled "Install MacOS Yosemite" will be inside your Applications folder. Make a copy of it in another location on your internal drive, some place where it is easy to find.
3. Next, of course, as I have previously stated, you'll need to check which third party software you have will need to be upgraded. You are good to go with TechTool Pro and SuperDuper!, but you will definitely need to get the version of Onyx that is compatible with Yosemite. You'll also need to check on the rest of your third party stuff, and download whatever updates you need.
4. I assume you have been making Time Machine backups. That's good, but as you'll see, once you use SuperDuper!, unless there is some compelling reason, you will not need to do backups with Time Machine anymore. I have never used it, and I have used SuperDuper! to 1) do some recovery, and 2) go through the process I describe below. It has always worked for me.
5. Download and install SuperDuper! on your Mac.
6. Do as much disk cleanup on your own as possible. Maybe get rid of some old files you no longer need, for example.
7. Run Onyx to clean up stuff on your internal drive. Also, use its Repair Permissions feature, and execute it. You'll most likely need to run the Repair Permissions feature at least twice, to repair just about all the permissions (interestingly, TechTool Pro also has a Repair Permissions feature, as does Disk Utility for all versions prior to El Capitan. I actually don't know which is the "best one", but I have always had success with Onyx).
8. Run TechTool Pro. For most of its features, you'll need to run them from the eDrive. I just run everything from the eDrive. Not sure how many of their features you execute. And for SSDs (like I have), a number of its features are useless (and in fact I do not run them at all, as they could do harm). A couple you need to do, assuming you have an HDD (versus an SSD), are File and Volume Optimization via the Tools section. I used to run those all the time when I had HDDs, but they are two of the ones I cannot run for SSDs.
9. OK, now you have a "clean, mean" system. Launch SuperDuper!, and backup/clone your "now mean and clean" system (I am assuming you have already dedicated a partition on your external drive for the SuperDuper! backup). Once that is done, boot your Mac from that backup/clone.
10. From that backup/clone, launch Disk Utility to Erase and Format (and if necessary, Partition) your internal drive.
11. Launch the file entitled "Install MacOS Yosemite", and perform a clean, fresh, "virgin" installation of Yosemite onto your internal drive. Once that is done, you'll be offered the opportunity to "migrate"/copy needed "stuff" from your backup. You obviously want to select the SuperDuper! backup for that.
12. Restart your Mac from your internal drive/Yosemite, and viola, you are just about there! A couple of things you need to to, though, at a minimum:
A. Install the new, Yosemite-compatible version of Onyx. The "old" one that was migrated (and compatible with OS 10.8.5) will not work.
B. You'll need to create the eDrive by launching TechTool Pro. The migration "process" does not "migrate"/copy the prior eDrive, but you don't want it anyway, as it is based on OS 10.8.5.
C. For any remaining upgrades of third party software, you would do that also.
OK, there you go! If you have any questions, don't be afraid to ask!