Because it's still a relevant topic since the holiday season is coming up and people are wondering what games they should get/ask for. Better to use an existing thread than for everyone who had the question to make new ones and clutter the forum.
With this point about the holiday season in mind:
I would say Fire Emblem: Three Houses is the best all-around game that has come out of the series for a number of years, and would encourage anyone who is actively interested in trying the series to give it a chance. Especially right now when it's discounted for Black Friday, if you live in a place that does Black Friday discounts anyway. This is especially appealing because if you do get the game and enjoy it, it maks the cost of the Cindered Shadows DLC more tolerable. As has been mentioned previously in the thread, there are four different story routes you can play, which gives it good replayability. The characters are lovable and the music's great.
Its main competition for modern widespread availability are Fire Emblem Awakening, the three Fire Emblem Fates games, and Fire Emblem Echoes: Shadows of Valentia, all of which were on the Nintendo 3DS. Three Houses manages to have both engaging gameplay and story/plot/characters, a balancing act that none of the 3DS games really pulled off.
Awakening's plot and characters are sort of bland compared to the older games, the gameplay can be fun but there's not much variety in mission objectives like in the older games, and most of the maps are essentially just big flat plains and aren't very complex. There's a popular aspect, similar to the fourth game in the series Genealogy of the Holy, wherein you pair up and marry members of your army, they have kids, and those kids become playable units once they're of age. In Genealogy of the Holy War, actual time passes in the story, while in Awakening the kids travel back in time to help their parents fight the game's main antagonist who has destroyed the future said kids were originally from. Popular because people like shipping and because you can make really strong, and some overpowered, units by inheriting specific skills from the parents. It started a pretty divisive split among fans when it released, which was only intensified with Fates, but which has died down since Three Houses' release. I fall on the more negative side, but others enjoy it.
Fates' story and plot stuff is worse than Awakening's in that they're actually just godawful and have nonsensical stuff like the baby dimension that they threw in to try to justify bringing back the marriage and child unit mechanics that made Awakening so popular. Fates Conquest in particular has a terrible plot but is at least well regarded for gameplay aspects. They also upped the pointless sex appeal fanservice from Awakening, which was never really a point of the series. I can't recommend them, especially not as first games, and would only say to try them if interested after playing other games in the series so as not to get a skewed impression.
Echoes: Shadows of Valentia has absolutely wonderful presentation and was the first mainline game in the Fire Emblem franchise to be fully voice acted before Three Houses. Its plot is the best of the three 3DS games by miles, it has great music, and the voice acting is enjoyable, especially for the character of Berkut. Unfortunately, the gameplay leaves a lot to be desired since this is a remake of the second game of the series, Fire Emblem Gaiden, and Fire Emblem remakes are generally very faithful to the experience of their originals. Which sounds good on paper and would be admirable in some ways, but things have evolved since the second game and the maps don't provide much challenge and aren't particularly interesting. I love the series and I really enjoyed my playthrough, but Echoes: Shadows of Valentia isn't something I see returning to for years because the gameplay isn't really up to snuff with the rest of the games. I'd nonetheless say it's worth experiencing, whether through personally playing through it or even just watching a playthrough of it or something, because it's still enjoyable in some ways.
That being said:
So I've been curious about FE3H. The only FE game I've played, though, I didn't like too much (Path of Radiance). If I didn't like that, does that mean I won't like 3H? (although tbh I don't remember why I didn't like PoR. Coulda just been I was a kid when I played it and it was a case of 'mad because bad')
Not knowing why you disliked it, I would actually say if you still have a copy of the game or access to it (though, given the circumstances, if it was your own copy I wouldn't be surprised if you got rid of it) to give it another shot. Path of Radiance and its sequel Radiant Dawn have one of the most interesting settings in the series and fun cast of characters, and the overarching plot of the two games is some of the better story stuff in the series alongside Genealogy of the Holy War and Three Houses. Granted, I'll admit bias, as Path of Radiance is my favorite video game. If you don't have it then probably disregard this for now, because you'd have to pay more than double the full cost of Three Houses to acquire another copy of Path of Radiance.
If you
do still have PoR, I'd suggest trying it again because you would quickly be able to ascertain whether you enjoy turn-based tactical gameplay. Because at the end of the day, Path of Radiance and Three Houses are both turn-based tactical role-playing games, as is the whole series. The genre might simply not appeal to you. That said though, you might also be one who might like the characters and experiencing the story and just see the gameplay as a vehicle to experiencing them, and I'd say it'd probably be worth playing Three Houses even if tactics aren't necessarily your cup of tea.
There's also Fire Emblem 7 (simply titled Fire Emblem) and Fire Emblem: The Sacred Stones, two games that came out on the Game Boy Advance which are available on the Wii U eShop, but even speaking as a Wii U owner I never really expect it to be likely that others will have the console. The reason I mention this is because you can get those games for like less than $10. Unfortunately neither are available for purchase on the 3DS eShop (though The Sacred Stones was a possible game download for 3DS Ambassadors), and since the Switch eShop doesn't have Virtual Console games, they're not available there either.