Borys, going by your general tastes/posting style on here and GAF (especially narratively), I can probably say you'd like the 3D Tales in the vein of Vesperia (though you don't have a 360, I guess) or Xillia more. However, since Symphonia has a PS3 version, I'd say give that a whirl before you even consider Xillia or Vesperia because then the jump between battle engines will feel more natural. You might draw parallels between it and a certain Final Fantasy game with respect to its story and I probably wouldn't blame you since it's kind of similar at first.
Symphonia's LMBS is essentially the shifting point as to when the series tried to get into 3D systems as opposed to 2D systems. Even to those who never followed its development or read up on anything any of the staff have said, you can pretty much tell because you're still confined to lines no matter what, and the camera moves like it's stupid. It wasn't until Abyss that free-run was added (hence its system was named Flex-Range LMBS), and a lot of people seem like they value that feature (I personally don't and I'm glad some games like Graces penalize you for using it too much). If you have a GameCube, I'd strongly recommend getting that version instead of the PS3 version, though. The PS3 version runs at 30fps which would hamper your technical progress in-battle if you're doing higher difficulties because it's based on the updated PS2 version. But if you don't care about that kind of stuff, go for the PS3 version since it's more accessible.
The reason why I chose Vesperia is because of
what I said here. The EFR-LMBS works well, and fatal strikes feel good. The narrative is more easily-accessible for non-Tales fans so it's a decent starting point for newer fans. It also looks very pretty, and
looks like how a Tales game in 3D
should look. It's the most consistent out of last gen's Tales games, but it's a bit too bad that you don't have a 360 and can't import the JP version for PS3.
I recommended Xillia because not only is it available everywhere, it's one of the biggest steps that Tales has made towards making cutscenes more fluid, using more mo-cap/full character models and more emphasis on better camera angles and scene direction. A lot of the soundtrack also works to facilitate the cutscenes because there are a lot of tracks on the soundtrack alone when listening in isolation that are suited more for cutscenes. The narrative is the focal point for Xillia 1, and it trims quite a lot of fat. I know Bebpo likes to joke that it's the Final Fantasy XIII of Tales (and I do too, honestly), but the comparison is fairly apt in terms of the changes that the studio made to focusing on cutscenes or the narrative focus in the game for the most part. Most of the fat in Xillia 1 and FF13 are in the postgame (despite the fact that you can fight Fell Arms bosses and do fetch-quest-esque sidequests during Xillia 1's main game), so on the surface, structurally both are semi-similar (you don't get into chapters in Xillia 1 with different castmates like FF13, though).
Of the recent 3D games, Graces f is my fave but that's because I loooove the combat and difficulty (so much so that I can effortlessly play it on the max difficulty), and how every single subsystem interacts with each other so cohesively (and thus have like three versions of it and platinumed it in both JP and English). But since the story's not great, the characters can be boneheads in main story scenes, and it opens with you controlling a fraction of the cast when they're children, I don't think it'd suit your tastes at all.
The reason I'd suggest for you to play them in order (ex: Symphonia -> Xillia) is because the games' engines in terms of cutscenes and especially their battle systems have continuously evolved. Going from Xillia to Symphonia might feel a bit limited because you won't be able to have as much freedom on the battlefield in Symphonia compared to Xillia. Cutscene-wise, Xillia's far more advanced than Symphonia for reasons previously noted, and the skits in English Xillia are voiced whereas in Symphonia they were never voiced so you're just going to watch heads talking in silence and you can't press a button to advance the text. But if you're just going in for the story, you can play them in any order you want. I just feel like your enjoyment might a little lessened because going from a modern Tales game to a game that makes transitions between scene direction/battle system versions to what we know as a modern Tales game feels really awkward. I know because I tried to go back to replay Symphonia after finishing up Xillia's Japanese platinum and it was really hard for me.
... I'd honestly be recommending Destiny R PS2 or Phantasia X PSP day and night since I think they're more consistent than the recent Tales games outside of Vesperia but those never came out in the west for you folks; and going by what a lot of recentish Tales fans have been saying, a lot of people don't like the 2D games much either. A lot of the 2D games were my faves. :'(
tl;dr: You'd like the Team Symphonia games more so go for Symphonia and Xillia since you don't have a 360.
If you're even thinking of Abyss go for the 3DS version instead since it doesn't run as crappy as the PS2 version does. But it's one of the worst Tales games to me.
