You’re right, I’ve been enjoying the Plex Media Server world for quite a while. My server now runs great on an older Mac mini with 4TB of storage. That might sound like a lot, but a friend runs Plex on a Windows system with 16TB of movies and TV shows. Like cloud storage, local storage today is limited more by your budget than by the technology.
For readers unfamiliar with Plex, it’s one of the most popular home media server platforms. It lets you create a personal streaming service, similar to Netflix or Amazon Prime Video, built around your own content. Many people rip DVDs or copy digital movies, often paired with a DVR app and a streaming subscription. Plex also works as a simple way to access hundreds of streaming channels and its own library of on-demand, typically ad-supported programming. You can get started by downloading the Plex client app for your smart TV here: Plex Apps and Devices.
Shortcuts: Start in Movies | Select by Genre | Fine-Tune the Collection | Save | Watch
The easiest solution is to use the filters in the Plex Movie view to shuffle all the films, but I actually prefer to create Collections and then use the ‘play a random film from this collection’ feature. Let’s have a look…
Start In The Movies Section
The easiest is to launch the Plex client – I do this in my Web browser for convenience – and go to the Movies section:

The top portion that shows “All Movies By Title 1704” is the filter system and it’s incredibly powerful. In this instance, it’s showing that 1,704 entries match the query “all movies by title”. Notice along the top that there are four areas in the Movies category: Recommended, Library, Collections, and Categories. Your wife might be able to just go to Categories and find Rom-Com, but my experience is that genre identification on content is less precise than it could be; hence “Collections”.
Before there are any entries in Collections, they have to be built. There are two types of Collections in Plex: regular lists and “smart collections” that are constantly recalculated as new media is added and other media is deleted from the server. I’ll advocate for the latter, but if you have an exhaustive collection of every Akira Kurosawa or John Hughes film and want to create a Collection, that’s not going to change much, so a regular Collection will likely work just fine.
Selecting Films by Genre
If you remember going to Blockbuster Video, you might think that there are a neat dozen or so genres in the movie world. Were it so simple! Nonetheless, you still can filter movies by genre as one of the many options with the selection tool. A click on “All” and a menu appears with oodles of choices:

Once you make a choice, if there’s a sub-choice, that’ll then be displayed. In this instance, known genres based on the existing media library:

Some of the genres my content specifies include Abstract, Action, Action & Adventure, Action&Adventure, Adventure, and so on. This highlights one of the challenges with a larger library: Inconsistent genre tagging. This is common in user-specified data tagging. For Action & Adventure movies, I have four matching categories!
One solution would be to laboriously go through my film library and fix each miscategorized entry (for example, I’m guessing it’s just one or two movies that have “Action&Adventure”), but that won’t stop new films from being missed in the smart Collection due to a mis-identified genre. Instead, I’m going to create a Collection that encompasses all four matching categories.

As shown above, I have 807 films in the “Action” category. That’s about half of my film library, so it’s an easy guess that’s a favorite genre.
With this as the foundation, it’s time to create a new Smart Collection. This is done by clicking on the horizontal lines with a tiny plus sign icon immediately after the dual-arrow shuffle icon. This brings up another menu:

You can opt to create a Playlist instead of a Collection, but Playlists can’t be “smart” so they don’t grow or shrink based on changes to the underlying media library. I’ll choose Create Smart Collection.
Fine-Tuning a Plex Smart Collection
Now we’re into the interesting ruleset area:

This should be familiar if you’ve ever created a filter rule in an email program like Outlook. Most importantly is the “+” adjacent to the “Match all of the following”, which allows the addition of additional rules.
For example, you could specify that only films that match genre = romcom and have a rating > 3.0 should be on the list. I’m more interested in adding other possible variations on the action & adventure genre name, so I’ll add a second rule for one of the other genre names:

At this point, there are zero matches because it’s set as an “AND” filter and a film can’t simultaneously match four different genres. Solution? Change it to an “OR” filter:

Logical, right? Once changed, it now shows that there are a whopping 1,066 matching films:

Can you see that number at the very top? That’s over half of my entire film library!
Save The Smart Collection
Now that it’s exactly what I want, it’s time to save it, which is easily done with the bright yellow Save As… button…

Same set of choices as earlier, so I could change my mind and make this a Playlist, but… nah. I’ll choose Save as Smart Collection…

I’ll give it a straightforward name, but you can, of course, use something like “Susan’s Comfort Film Library” or whatever else fits best for your circumstance.
Watching a Random Movie from a Collection
All the heavy lifting is done, and the new smart collection is ready to enjoy. Access it by going to the “Collections” tab in the Movies section from the four Movies areas along the top:

You can see that the new collection is leftmost, but I also have collections by decade as well as genre. The montage graphic is automatically created by Plex from the contents of the particular collection.
A click on Action & Adventure and more information is revealed:

Did you notice that the movie posters have changed? It’ll update that every time you view the collection, which is how I realize that Action apparently encompasses both Bad Boys II and Scooby-Doo in my library! I might go and recategorize the Scooby-Doo movies as ‘animation’ to clean things up; since it’s a Smart Collection, the recategorized films would then vanish from this collection.
To finally get to the desired capability, a click on the dual-arrow shuffle button will randomly pick a film out of the collection and begin playing it. In other words, any of over a thousand films in this collection will start playing with a single click. Mission accomplished.
Pro Tip: I’ve been writing about my Plex server setup and configuration for quite a while. You can find the articles in my Computers & Internet Basics area or simply search for Plex at the top of the page.