One of my favourite fighting games ever!
I was never really too fond of team-fighters but this one really stroked the itch. Great Soundtrack, great characters, and especially a really good fighting system. On first view it may look really basic, and it is at the bottom, characters don't have many moves and it is easy to play new characters you don't know and have success with just playing at a basic level. That's why it's imo also a great game for not-so-well-versed players, the game has a ton of defensive options and is easy to understand at the ground. There is also a good training section and probably the best training mode there is. Also replays are there, and a silly but enjoyable visual-novel style single-player mode. The characters all have a certain charm and personality and it is basically given that everyone will find their favorite in there (even if they have to have dlc).

But it is also a really deep game, where the detail is in the fighting system itself instead of the characters. You can make different combinations of characters and use their assists to enforce your certain playstyle. Want to be an endboss? Play team big-bois with Tager and Waldstein and be a grappling menace. Want to be zoners pure? Go with Vatista Nu and let them hate you. Or just a pure mixup team? Or Team counter? There's a lot of fun to be had trying out combinations.
Then there's also cross-combo which is just crazy, you can play both characters at once and when you figure it out, it opens up even more possibilites and mixup options. Super enjoyable game to watch and to play at every level, which is often rare for a fighting game.

There's not all that's sunshine though, the balancing needs some work as some characters are just overtly at a disadvantage while others will never be bad. Be prepared to like a character and find out that you've chosen the struggle-tier (yes, Noel bad). There's also no arcade mode and the AI is kinda weak even on the highest level as they don't use assists and such. The price-point is also kinda lame, considering there are a lot of characters as dlc and most sprites are taken from other games and low in quality. It is fair, when you like the game, but for the content it could have been a good 10 bucks less.
Online is also atrocious, they fixed it a bit so you don't get disconnected as often, but it is blazblue crap netcode meaning you gotta let the intros play so the game can sync (and no, it doesn't stay synced). It is not SFV unplayable crap but also not Uniest goodness, kinda at the level of Tekken. 3 Bars gonna be a 50/50, and sometimes you can have 2 bars that are perfect and 5 bars that are horrible. Also it's an anime game so expect ranked to be dead and sometimes having to ask at discord for matches, but it has a great community.
Also ArcSys seems to have it on-hold since a while, they teasered a fifth fate but that has been months ago and no patches or anything since then. It has potential to be the most interesting team fighting game, and ArcSys is not known to leave their games alone, but one grows to be a bit disappointed by the silence.

Basically, if you like teamfighters or even if you don't and if you are a good or a new player and if you don't mind anime asthetics and the other minor caveats, I suggest wholly to you. One of the best fighting games I've ever played and I think it's hard not having fun with it.
Buy it on a sale. You don't need the DLCs as there are a lot of really viable chars already in the basic game but they are also great, buy them too if you want to play it for longer (to train matchups or get more options etc.)