Storage is key.  I have 40 TB of storage on my Plex server - about 10 TB is actual media, then that's mirrored - and I have basically another 10 TB to add to it and 10 TB to mirror.

Of course I have hundreds of movies and TV series.

Rip your media to .MKV x265 for smallest files.

You could use a mini PC, but you're going to need storage.

Agreed about the storage being the biggest concern.

For smallest form factor, the intel NUC was basically laptop hardware, without the keyboard/screen/camera/speakers, stuffed into a tiny little case.  You could get the cases that allowed 2 HDDs.  That's easily 10TB of internal storage.  About 6"x6"x4" form factor. You only need the keyboard/mouse/screen while doing the initial setup.  After that, you can run headless.  Intel discontinued the NUC line.  There are plenty of clones and knockoffs.

Synology has smaller NAS products. They are designed to use 3.5" HDDs, so they'll be larger than a NUC.  But much easier to setup, as they are designed to run headless right out of the box.

I would just go with one of those and then a USB DVD drive when you need to rip a disc.

I have to say, though, I dont understand the need for a portable plex server.  If you set it up right, your shows are accessible across the internet.  And, in fact, plex acts like a shit head if it doesn't have the internet.  So why not forget the requirement for being portable?  Just make the server so it meets all your other requirements.  Then configure the server and your clients to be able to access your shows across the world-wide-web.  Making it portable seems like it'd just act to gimp the thing, and you run the risk of damaging it.

If you're a printer fanboi, somebody at work sent me this.  Its a configurable NAS/plex server type of case.  You build one to exactly fit your needs.
https://www.printables.com/model/590711-mass-stackable-nas-itx-enclosure

OP if you have a PC with Blu-ray drive to rip and encode the movies the initial time, then a 3-4 drive NAS than can run Plex might fit the bill the best IMO.  Small, multiple drives, fairly self sufficient.

A SFF or micro PC won't have the storage capacity and might not have the CPU needed to do that first encode in a timely fashion.

It really depends on the use case.  The types of files plex is streaming and whether or not it has to encode them.

For years, I used an odroid as my plex host.  Its an ARM based single board computer.  Basically the same as a samsung galaxy s5 cell phone, with AC power and USB3/ethernet ports.  With that setup, plex was able to stream 99% of what I needed it to.  The only time it shat the bed is when there was some video file with external subtitles.  Those needed encoded in the video, and the javascript layer of plex refused to even try, because it was an ARM CPU.  I edited the javascript to remove the limitation and it was able to encode the video with subtitles fine.

Just about any x86 host that uses anything better than an atom CPU should be able to handle encoding and streaming a couple streams.  Especially with a plex pass membership that lets it use hardware encoding.

I have a synology NAS that runs a plex server, and is used for my laptop and desktop backups. Works great. Only limit is your budget. You could consider it portable, I just have the a 4 disk setup. anymore drives and it'll be pretty big though. Easy maintenance, just had drive fail and popped in a new one off Amazon. On Newegg you could do a synology + drives for about 32TB of storage for $1500, less if you try to find deals on drives.

True, if you're not trans coding or have a lot of streaming clients the requirements are far less.  I was also addressing the desire to rip/encode from disc on the same box.

OP the desire for it to be "portable" is part of why the NAS suggestions are there.

You may want to research that a bit before you make a decision on having a portable plex server.  Search for phrases like "how to use plex offline".  It does not work like you'd expect right out of the box.  Its possible, but requires fiddling with the advanced settings, and knowledge of the network before hand.

I'm using a ~10 year old PC with a 10TB external drive. Works just fine. I would think a modern SFF would be perfectly ok, and USB storage can certainly work.

If you're doing direct to TV/monitor, then you dont really need plex.  Now you're just talking about a tiny computer.
The aforementioned NUC computer, I have one of those connected to my TV with an HDMI cable.  You can pick windows or any linux distro that makes you happy.
For the keyboard and mouse, I bought a remote for that.  You hold it in your hand like a normal TV remote and point around to move the mouse.  And you flip it over and there's a qwerty keyboard.

There are a million other products out there for this, too.  I have used the WDTV and an OUYA game console, both purchased at the local best buy for about $100 and have enough power to watch movies off.

It is possible to set up a Plex server to run on a local network without Internet connection.  The instructions are on the web.  It has to be done before the Internet is out!

The real usefulness of Plex is streaming your media to wherever you are, it's kind of the point.

The lifetime Plex Pass adds a lot of versatility.

My Plex server is a re-cased Dell 9020 tower (i7-4790) running Win10 that was basically a project (originally I was  using a Dell SFF Inspiron 3647 with an i5).  Most of my HHDs were repurposed.  You don't have to use bleeding edge hardware.

OP, do you have an idea of how much storage space you're gonna need? And are you going to transcode videos on the fly?

If you're not transcoding (instead simply streaming in the video's native resolution), any Core i3 or higher will be just fine.

If you want to do a small NUC sized machine, you'll be looking at NVME hard drives. The 2TB drives are pretty reasonable. There are 4TB, but they're much more expensive. None of these are likely to have a Blu-ray drive, as it's too big. If you were able to rip/encode on a regular desktop and transfer to the small machine, it would be very portable.

Look at some of these for inspiration

Otherwise, any of the Optiplex SFF or similar will work fine. They're just a lot bigger. But they would have room for a 3.5" hard drive and a Blu-ray drive.

I'll make a potentially unpopular suggestion here. Don't bother ripping and encoding your Blu-rays. It'll take forever. Simply download them from your favorite pirate site. You bought and paid for them. I have zero ethical dilemma with downloading the same movie and putting in on my Plex. This is the same result end result as ripping and encoding.

I run plex without the internet when it goes out.
I have it setup to stream still.
we have 4 roku's around the house and I have one I take with me on trips.
when the internet is down, I can still stream inside the house to all the tv's.

if you don't actually care about streaming to multiple places, then I agree with a post above, you really don't need plex, BUT it really makes life easier.

I used to run a stand alone pc that I had HDMI out to a tv nearby and could play all my shows from that.
there are some free ware type plexish stuff to at least make it easier to organize your stuff, so you aren't just digging around windows on a tv and playing via media player to the tv.
microsoft even made a package for that back in XP but gave it up shortly after vista.

I cannot tell you how much easier plex is for all of that. I got one of those lifetime passes for 100 bucks when they went on sale one year.

the other nice thing is I had video capture cards for OTA and cable which I now use to record local programs off an antenna. which I guess you would need internet to set up the guide, but I think you can vcr it as well.
unless you are way out in the boonies with no broadcast tv either.

HDD are going to be the expensive part.
even with an inexpensive 4 hdd nas, most of my 1k spent on it was just HDD.
for my plex server I have 4 drives in it.
I don't know how you would even do that with a small form factor due to power supply alone.
external is ok, but remember transfer speed and the drives going to sleep.
also don't forget about shucking drive enclosures for larger drives cheaper.

as for security camera dvr, just buy a purpose built one for that, don't try to combine.
the hdd you are using would have to do 2 different things well.

for your plex it would be reading a lot, but writting very little.
for the security feed it is writting a lot and reading very little.

Not unpopular with me - just use a VPN.

Ngl, idk if you'll be able to do that on a below 400 budget

Yeah, here is all the budget: https://www.newegg.com/seagate-ironwolf-pro-st20000nt001-20tb/p/22-185-071?Item=22-185-071&cm_sp=product-_-from-price-options

Do the ripping on a pc.  Get a Synology NAS and at least do mirroring to protect against bit rot.  Synology is one of the best small form factor, low power, and easy to use options.

For anybody keeping score, me and the boys at work did some tests.  For a NAS, by far the biggest use of energy is the disks.  So your energy usage ends up being a factor of the amount of data you access, the size of your raid array, and how much your drives use.  Overhead costs to run the CPU and OS is next to zero for things with no screen or GPU and small CPUs.

My synology is a 6 disk array of WD gold drives and the rizen CPU.  We use it fairly heavily for plex and backing up about a dozen computers and phones.  It uses 2kwh of juice per day.