Both titles included in Zero Escape: The Nonary Games are excellent visual novel/puzzle titles. Even with my limited experience in the genre, I cannot recommend them highly enough to anyone who has the patience to watch a mystery unfold in a methodical, but ultimately satisfying fashion.
However, I find it difficult to describe why the plot is so engrossing without dropping several major spoilers about the game's structure and themes. Hopefully I can slip the recommendation in successfully around this spoiler minefield.
Nine Hours, Nine Persons, Nine Doors

After some brief exposition, 999 wastes little time getting you into the core gameplay of the series: solving a puzzle that will allow you to escape from a room. The puzzles ramp up in complexity and sheer size as the game goes on, but I rarely found myself stuck for more than a few minutes at a time. They are challenging but not overwhelming, and aside from one instance I was never frustrated enough to stop playing the game.
999 also has a subtle hint system if you're truly stuck. Examine an object or item in your inventory enough times, and a character will say something like "Didn't we see somewhere we could use this?" or "Maybe we don't have enough clues" to help you along. The puzzles are basically as difficult as you want them to be; examining things enough times will essentially drag you by the hand to your solution.
I only had to take notes a few times, which will probably look like complete gibberish if you haven't completed the game.

Despite the puzzles being the core "gameplay" over 999, I've described less than half of the game here. It is a visual novel, and the "novel" part is serious. You'll be reading a lot of text and hearing plenty of long speeches on your way to the ending(s).
Luckily, the main cast of 999 are more than capable to support the 30+ hours you'll spend with them. Everyone trapped on this ship are mysteries to be unraveled, with bits of their backstories and personalities being doled out steadily enough as you build trust for them. Even the less sympathetic characters have some quirk or trait that endeared them to me. It makes the endings even more resonant as these people start revealing their true colours and get thrust into mortal danger.
Or thrust the others into mortal danger.
The English voice cast are excellent, sounding completely genuine even during the late moments of intense melodrama. The script is tight, full of funny easter eggs and jokes if you poke around at certain items or locations a few times.
Most of the negatives of 999 are related to the user interface. Every button on the directional pad is mapped to a different menu function, like the story-related flowchart, a calculator, items, and files. However, you have to memorize them because the "menu" telling you what button does what only appears occasionally.
The game was ported from Nintendo DS to the PlayStation 4 version I played, and it shows occasionally. Clicking on small items in the world, and the finicky menu navigation would probably have been easier with a touchscreen and stylus.
Zero Escape: Virtue's Last Reward

Virtue's Last Reward follows the same basic structure from 999: longer story segments broken up by Escape Room puzzles. But this game is bigger and more complex in nearly every way. Full 3D models replace drawn art, there is much more voice acting overall, and the game is longer with more complex puzzles.
Some of these changes were easy to adapt to, others less so. Switching to 3D models was jarring at first, and the lip flaps almost never match the English voice acting. There is also the occasional issue of characters making weird faces, holding their mouths open for too long or teeth clipping through faces. They look fine for the most part, but seeing Clover's weird frozen open-mouth smile did creep me out from time to time.
The menu issue with 999 has also been sorted out. On the PS4 you can bring up a menu at any time with the touchpad, eliminating the need to guess what d-pad button you want to hit.
The subtle hint system from 999 is now a selectable difficulty. Easy Mode will give you detailed hints on puzzles when you attempt them and fail enough times. I preferred to stick to Hard mode just to have the satisfaction of solving puzzles on my own.
However, VLR's puzzles are significantly more complicated than 999's. Compare my brief note sheets I took during 999 puzzles to three nearly full pages I wrote playing VLR. The puzzles require more math, memorization, and occasionally jumping back to earlier rooms to recall key words or information. There's no way to save some things with an in-game notepad, so I would highly recommend taking notes on any VLR puzzles that have too many things to remember.
Unlike 999, I found myself frustrated and stuck on puzzles more often in this title. One room in particular (the PEC) had such an esoteric solution that I had to use a guide to finish it. It only happened 3 times, but there were puzzles that I had no clue how to even approach without a slight hint.
What did I do to deserve this ? #PS4sharehttps://t.co/Ju3ht6Ajqb pic.twitter.com/3B4KU2MvPm
— SURT (@PerfidiousSinn) October 5, 2017
Of course, solving puzzles is only a small part of this game. In fact, I was more excited to see the twists the story took than indulging in the brief endorphin rush you get from cracking a really tough riddle. The plot of VLR takes basic premises from 999 and flies thousands of miles away into some silly but immensely gripping sci-fi drama. The voice actors are even better in VLR, and the script is full of charming moments and jokes that got me to legitimately laugh more than once.
Sigma making a flurry of cat puns whenever he can is bizarre, but his cohorts reacting to them with confusion and anger makes the bit worth it.

I may have brought up flaws with the puzzles, but I still only have the highest recommendation for Zero Escape: The Nonary Games. 999 and VLR are about the story first and foremost, and they are fascinating mysteries to unravel. The voice actors are excellent, really a step above voice acting in most other games I've played.
The script gets heavy into scientific concepts and long-winded explanations, but also keeps things light with some goofy jokes and puns when necessary. I was constantly compelled to see one more ending and get one more piece of the bigger picture. And each game wraps up with a satisfying conclusion, raising some impossible questions and paying them off at just the right time. The games are long, but the pacing always kept me hungry for the next reveal all the way to the final sequence in VLR.
If you have the time to see a story raise several impossible questions and pay them off in the most satisfying way possible, The Nonary Games are mandatory.