Short answer: Yes, you can play all the games and probably enjoy them, but the last one, the one that
is and
is not canon (Danganrompa V3), is the worst of all in almost everything, and you don't need to play it to understand the story, even if it explains how the story has been and is for all the games, which as a story resolution, I think is stupid one.
REALLY long answer:
I will try to make a fair review. I have completed the four games (but this collection seems to only have 3 of them) and seen the anime for both the first game and for what it is the resolution of the saga (I will explain this in more detail in a while).
What will you do most of the game is
read, exactly like 999, but it doesn't have these kind of "minigames" (which in 999 are escape rooms), but it has something called "
CLASS TRIAL" after each certain action happens in each game, and (at least for me) this mechanic is garbage (only when you need to play, when you need to read it's fine), so if you don't like to read and prefer something more "action based", these are not your games, but since you named Ace Attorney and 999, I will pretend that you actually like to read, and at this part, is amazing. The story, the dialogues (that are not part of the story)... are really fun overall. I really recommend them.
Now, in a more in-depth review, I will try to explain briefly (and without spoilers) each game.
The first one,
Danganronpa: Trigger Happy Havoc, is great. I really loved the story and the overall game (excluding, of course, that stupid CLASS TRIAL mechanic).
I am the kind of person that can see that something will have a "plot twist" before it happens, but in this game (and probably because it's the first Danganronpa I played) had some of the best plot twists I have ever seen, and the best part is that I couldn't predict them, for example, in the second class trial.
The characters, some of them, are horrible, in my opinion, some of them because they look like "fillers" or lack the "charisma" the other characters have. I don't know, Even if they play a part of the main plot, I feel like if they didn't exist, nothing would have been different (even of course, that this isn't true, but it's a feeling a have).
And again, this is the first Danganronpa game I have played (and the first one in the servies, but it's
not the first chronologically, but the first you should play),so that could be the reason I found it amazing and the one that made me end with the best feeling of all the four games, even when the second is clearly better).
It also has an anime that explains the base story pretty well, but the game has some details that even when they're not very important, you might want to know them.
The second one,
Danganronpa 2: Goodbye Despair, is amazing. Almost all the characters are great, and how they develop their story and the main story is great too. It has one of the best characters of the entire Danganrona universe (N. K.) and the best character resolution for a certain character of the whole Danganronpa universe.
The game story is great, but at the end of the game, you end thinking if the writers were smoking something when they were doing that specific part. It also has CLASS TRIALS, the only negative point, as far as I can think at the moment.
The third one,
Danganronpa Another Episode: Ultra Despair Girls, (I am not sure if its the third game released, but it's the third game you should play) is... Mostly different of the other games. The mechanic changes from a visual novel to an "action" game. It happens between the first game (Trigger Happy Havoc) and the second one (Goodbye Despair), but you shouldn't play it until you completed the second one, because it features a few things of the second game that you will not know nor understand (even when the second game has nothing if I remember correctly, that links it to this game, but as I said, this game has some links to the second one). Its kind of difficult to explain without spoilers, but what you need to know is that you shouldn't play it before the second game.
The story is okay, I guess, but its not the best in the series.
It's not that bad, but if I could go back in time knowing what I know about the game (not the story, of course), instead of playing it, I'd seen a recap or something like that in Youtube.
The fourth one, they are actually two, and they are not games, they are anime only, one that explains what happened before the story of the first game (which is linked to the main plot of the first game and the overall series) and another one that happens after Danganronpa 2. You should watch one episode of each every time, starting with the one that happens after Danganronpa 2, but you could watch one entirely and then the otherone, but I don't recommend it.
The names are Danganronpa Future Arc (this is the one you should start with) and Danganronpa: Despair arc (which is the second you should look at).
Finally, the fifth (or sixth if you count the previous as two entries) entry is Danganronpa V3. Which I didn't like it very much because breaks one of the most important rules of the previous games: Even if the bad is bad, he doesn't allow anybody to cheat, even itself, and in this game, sadly, this happens. And this is not the only thing I didn't like, the overall cast is horrible, and the only real reason I'd say that you should play the game is because of the ond and only, almighty character,
Kokichi Oma.
This game happens after everything else has ended and even it acts as a "resolution" of the whole story. More or less. I find it that is more a lazy way to finish something that anything else, but there will be people
mentally ill that really enjoyed the game.
It will take you a while to finish everything, but I do really recommend them. The overall feeling of this series was very positive.
Sorry for the long post and hope you find it useful.