First I would work on whats limiting your current setup: e.g. CPU, RAM, storage
I have ODROID XU4, HC1, HC2 here. They are EOL but run without problems for years now with (not inside H2) one 2,5" disk chucked from Seagate external drives.
The drives are fast enough to saturate 1GBit LAN. They would improve a little (20% ?) if I had all 2.5GBit components.
SSDs would only give you a quieter setup at a huge price and no noticeable speedup.
These ARM-machines I have would not be the best in your scenario because of RAM limitations (for many Docker containers) and I guess low CPU power (see my first sentence). They run at 5W though...
I use Syncthing (native - no Docker) for my files and Baikal for CalDAV and CardDAV syncing. I guess it would be no difference in speed if I had installed them via Docker.
In your case I would go for the H4+ as a cheap option or something like a Fujitsu Q556/2 ( mischka ) or a used notebook you might have around.
I would not bother about eMMC because of their low capacity and inferior speed compared to an SSD. If you use spinning rust for data eMMC could be a good choice for OS and applications. Here I used micro SDcards in two devices and eMMC in one device. One SDcard died so far... eMMC is more robust.