Aside from a fairly weak main plot, the games individual characters are pretty fantastic. You can build relationships not only with yourself and the others but between the different characters themselves. Not every possible interaction between the characters is great, but I find most of them to be very enjoyable. Characters like Raphael and Alois, for example, end up being two of the most likable characters I've seen in a game in ages.
Dmitri especially had a fascinating story, even if it felt awkwardly unresolved by games end. The game hints at this from the beginning, but despite his noble and kind intentions, he struggles with a rather extreme bloodlust when something pushes him over the edge. A big part of the story is helping him learn to deal with that and the survivor's guilt that leads him to this point. Claude may be my favorite house leader overall, but Dmitri's story ended up being the most interesting.
The last thing I will note about the story is the world-building feels very weak. You pretty much never leave the Academy outside of battles, and the game doesn't really give you much on what kind of world you actually live in. I never get a real sense of why some of the game's villains fight, as I have no clue how much their motivations were justified. There are plenty of things I could tell you about Fodlan, but only because other people said something at some point, not because you actually get to experience any of it. That is where the game's story ends up being at it's weakest.
On to the gameplay, there are two major sections. I'll start with combat, which I enjoyed quite a bit. While weapon strengths and weaknesses do play a part still, I feel like it's more about how well you strategize than what weapons your characters happen to have on hand.
Weapons wear down as you use them, though you can have multiple weapons equipped at any given time. That said, to much gear can start to have an effect on your speed stat, though increasing the Heavy Armor skill of a character can mitigate this penalty. It does force you to be a bit careful about how much stuff a character is lugging around, especially if they have lower strength or are pretty poor in regards to Heavy Armor.
That said, this is by and large a pretty straight forward SRPG. Spells have a certain number if times they can be cast, weapons wear down, and each 'team' takes moves all their units on the same turn. The only other major thing to really note about combat directly is the Time Pulse. Something goes wrong for you in battle, so many times per battle (There are ways to increase the number) you can reset time by quite a large amount in order to undo what happened and revert the game-state back to what it was a few turns ago. It's kind of nice considering how easy it is for characters to fall in battle in this game, even on normal difficulty. Though I do feel the game can get a bit over-generous with how many times you can do this by games end.
Aside from the combat itself, you have skills characters can raise. Each kind of weapon has a skill, black and white magic each have skills, Riding, Flying, Heavy Armor, and more have skills. They all can be raised by using them in battle. Increasing their Rank unlocks passive and active abilities to make using that weapon more powerful, as well as being able to use higher-end versions of those same weapons. Though there is one more reason to raise skills, unlocking classes. As you grow in level, you can start unlocking advanced classes that affect your stat growth and what your characters can do. In theory, with a couple of exceptions, any character could be pushed towards any class you want so long as you raise the proper skills. There are some characters whose base stats make it obvious making them, say, a mage would be a poor choice, but there are still multiple options you have for anyone.
Of course, certain classes require Riding, but as your starting classes have no horses there is no way to increase a characters riding abilities in battle, and that is where the second portion of the game comes in. At the Academy between missions, you can take the time to build bonds with other students and professors, as well as instruct students. There are a few ways to do this, but the short version is you can select what abilities characters train while not on a mission, and this is how you get characters into unique classes that they would not otherwise have had access too. Bernie, for example, I wanted to keep on the Archery bath, though the highest rank of Archer is 'Bow Knight' who rides a horse, whereas no other archery class does. This means you would need to train her up in Riding for quite a long time to get that skill high enough.
Beyond training your students, on certain days you have the option to explore the campus. You have a limited number of actions you can use to get to know your students, motivate them to help with study, build bonds between students, or train up your own skills by speaking with the other Professors or Knights. You have quite a lot to do during this time, though it does end up being my biggest issue with the game.
Seeing the campus constitutes a large portion of the gameplay, and there are items you can find around the campus on different times of the game meaning you will be re-exploring the same place several times by the end of one run-through of the game. It's a nice idea, but so much time is devoted to such a repetitive act after a while it really starts to drag the game down. Even when things go down for the games second half you don't get to escape this campus. In addition to making it a bit hard to get a feel for the world you live in, as stated earlier, but even a single playthrough I find myself getting bored of this portion of the game. But considering how useful it is for building bonds, it's not really something you can skip.
In the end, I recommend Three Houses. It certainly has its share of problems with portions of the gameplay and an overall weak narrative, but the cast is fantastic and the combat is solid and stays interesting throughout the whole game. It's not a game that I think is going to be some all-time classic, nor does it entirely escape from its own shortcomings, but I had quite a bit of fun on both play-throughs of the game. Definitely worth picking up if you are a fan of JRPG's.