Running Plex on the same device as your media file storage SHOULD improve integration and performance (make sure it has the capacity and is not under-powered, particularly if you want it to transcribe video codecs when streaming).
Which Plex server version you use depends on how you install it. There is (FreeBSD) Plex plugin for FreeNAS. If you install it in a VM under FreeNAS it will depend on the OS of the VM.
The key to dealing with technophobes is to ensure that the user interface is a simple as possible (I think Plex largely ticks that box once the setup is complete).
If you do not have Linux, FreeBSD (or some other unix) type experience, I’d recommend that you first “try before you buy” and install FreeNAS in a VM and set up a new Plex server. If you are comfortable working thru FreeNAS and working in FreeBSD, then move the installation to it’s own dedicated hardware platform.
My Background & Experience (for context)
I have FreeNAS running on a FreeNAS Mini XL. This gives me a very robust FreeBSD installation with ZFS. All my media files sit within a file-share on this system (similar to your media sitting on a Synology NAS).
Under FreeNAS you have the option of running Plex as a plugin or in a jail (FreeBSD version of a container) or in a virtual machine (VM). Running Plex on the same hardware as your media file store presumably reduces the potential for network lags across the system. I have it running in an Ubuntu VM.
In my living room (with the big TV & sound system) I have a Roku with a Plex client installed. This is how I access a lot of my media.
I also run a Plex client on my laptop in a browser and have the Plex App installed on my iPhone
These clients are about as simple / straightforward as you can get (although navigating a multi-component media system with multiple remotes is not trivial and was something my wife refused to use by herself for several years…)
While I have a lot of experience messing around in different system, after 25 years of occasional Linux / Unix / FreeBSD use I am still really only a novice & I prefer GUIs to command line interfaces.
My experience with FreeNAS is:
(1) it is not novice friendly,
(2) while knowing Linux can help (and lead you astray) FreeBSD is not Linux and I think that the learning curve is steeper,
(3) very few projects work straight out of the box, generally some hacking and mods are required,
(4) upgrades to the OS can, and do, cause projects to break.
So (with the benefit of hindsight), I’d only recommend FreeNAS to someone with a high level of experience and the time and willingness to tinker under the hood.
While many (YouTube) commentators / reviewers regard the FreeNAS Mini / XL hardware as over-priced compared to “roll your own” option, it is a very neat hardware package and has proven itself to be VERY robust and capably of surviving frequent power-outages without further user intervention (as opposed to various Linux installs that fail to even regain a network connection after an outage). It just bounces back by itself!
The FreeNAS Mini XL is also fairly compact, looks smart and is reasonably quiet (different reports suggest your mileage may vary). The Mini takes 4 drives and the Mini XL takes 8 drives. This makes it a reasonable entry level server with more breadth of capability than a standard dedicated NAS. But it is not cheap! My FreeNAS Mini XL cost me around $2500 once I’d put 32 GB RAM and 4 WD 8TB drives in it.
Why FreeNAS? - integration with ZFS is probably the number 1 reason (if you are not using ZFS, then there are other contenders). Second reason is the GUI which keeps you out of the command line and script files a lot of the time, but does not always get you where you want to go. There is also an active & good help forum.