As someone who has never played a Persona game but has always wanted to, are Persona 3, 4 and 5 all solid games?
Big post will become lost, but eh
The Persona games are excellent games and fun time sinks. In my personal opinion; P4 > P3 > P5. All of them have a fun cast, a cool setting, awesome music and some cool stuff like social links, Persona/Demon fusion and cool boss battles. The only bad parts are some problematic takes on LBHTIQ characters, the most disappointing story imo with Kanji in 4. Some people also don't like the school/jobs/social link/going into dungeons as it takes some time management, but that's more of a personal thing.
In regards to the games themselves...
Persona 3 (I played the FES version) is a good game and a great introduction to the series. The core cast is good, the setting moodier compared to the other two games, but ultimately its a great ride. In terms of QoL P3P might be the least "accessible" title of the three as P4 and especially P5 are far modern games, but even with a bit less smooth experience P3 is an excellent game. Honestly I have wanted to replay 3 for a long time, so insert Akihiko meme "I've been waiting for this!"
Persona 4 the Golden (PC) In the end the best Persona game. It's a game where the core cast has a bit more zip in terms of characters and they're a fun bunch overall. (Rise is only thirsty as fuck) And yeah, I personally love Kanji, but the handling of his sexuality should have been better. Way better. It has its silly Japan tropes, but as a game to play its really tight, I feel the game offers more freedom than a P3 or P4 and more importantly the music is pretty damn good. It also has the protag living with his uncle and niece, who have a really cool dynamic with the protaganist. I have the Golden on PC, but I really want to replay it on Switch. That's how much I like it.
Persona 5 (both vanilla and Royal) in the end ranks third in my list, but do not let that stop you; Royal is the definitive version because Morgana backs off a bit and doesn't order you to sleep. It a great refinement of the previous Persona's; it has a fun cast, the dungeons are pretty cool, the extra content in Royal is cool and more important, the music is amazing. Life will change, Rivers in the Desert, Last Surprise etc. are extremely catchy. Plus Persona 5 has, one can not deny it, style.
Hope this helps!