What are my best options? Build something myself with current hardware?
Build something based on a MicroATX board with a CPU > i5-6500, this will probably cost around 80€ second hand with RAM. Server hardware is overkill, wastes power and older CPUs are always worse in all possible ways. Even if the board only has 4 SATA ports, a PCI to 5 SATA port card and it will be enough. Use BTRFS as your filesystem and its RAID if needed.
You may be thinking something like “I want a faster CPU in order to have fast SMB”, don’t. Your gigabit network will saturate before your CPU or even mechanical drives and when this happen you’ll get something like 10-20% CPU usage. Just don’t waste your money.
From a power consumption standpoint are SSD’s better than HDD’s? It depends on the hardware, either way is isn’t feasible to have around 20TB of SSD storage. Even considering you can now buy a 4TB SSD for 195€ that would be a lot of money.
Syncthing is a very good piece of software, to sincronize devices with a NAS - except if you use iOS. Currently I’m running Syncthing on my NAS and all my devices sync to it (no cross-device sync to avoid issues). Then I’ve an SMB share to allow access to the files on iOS devices and FileBrowser for a cloud-like web browser access experience. Works flawlessly uses very little RAM and its solid, private, secure and manageable open-source - not something like Nextcloud that calls home, breaks everything on upgrades, wastes ram and runs slowly to only deliver an inferior experience in all possible ways.
Running stuff in your NAS: if you’re really into a low power solution you might want to stay away from Docker. Simply install a clean Debian system and manually get what you need instead of tons of containers and dependencies. This will allow you to run more stuff on less hardware. Linux isn’t that hard, you can do it.