Regarding the Synology:
What model?
You do not mention how you are moving data to/from the Synology, but it should not be slow or laborious.
You can map shared folders on the Synology to your PC. For example, /media on the Synology could appear as M:\ on your PC. Moving files to/from the Synology is then the same as moving them between drives or directories on your PC. This also makes organizing files on the Synology easier, as you can use Windows Explorer instead of Synology File Station. You can have multiple Synology shared folders mapped to multiple PC drive letters.
Your PC should have a wired Gigabit Ethernet connection if possible. A wired connection will be much faster than using WiFi. If it must be on WiFi, then a 5 GHz channel is preferred. WiFi on 5 GHz is much faster than on the 2.4 GHz channels.
Regarding Plex on the PC:
Shutting down your PC when you are out of town, etc will not cause problems with Plex Media Server.
Starting up and shutting down the PC several times a day, the normal usage pattern for most people, does cause problems for Plex. It does not leave time for background tasks to run and some tasks may be interrupted and not complete.
You just need to leave time for background tasks to complete. You can schedule the tasks to run during the day when your PC is turned on (Settings → Scheduled Tasks). Not all tasks stop at the end of the maintenance window. Some run to completion. So, it is still best to leave your PC on as much as possible.
Let me know if I can be of further help.
