It has a ATB meter. Just because it has free roam and gambits doesn't mean it isn't turn based. You don't need your party on one side and the enemy on the other to accomplish that.

I'll go ahead and say that the best place to start getting into the genre is Final Fantasy...
WIth the consoles you've got you can try FFVII, VIII (though I wouldn't recommend it), IX, X or XIII. Maybe you can try to find the GBA versions of IV, V and VI, though I'm not sure how expensive they are.

Other than that, Chrono Trigger is one of THE best games of all-time, imo, and there's the DS port (and I think it was released on the VC, though I'm not sure). Ni no Kuni is pretty damn good too. Super Mario RPG (I think it's on the VC) is a good starting point too.

Edit: Oh yeah, The Legend of Dragoon is pretty fucking good. It's a PSOne Classic on the PSN

I think you're using a loose definition of turn-based for that, but I'll concede.  Final Fantasy 12 is just too good a game.  I suppose any Final Fantasy games other than 1, 2, 3, and 10 aren't true turn based anyways.  

Radiant Historia (DS)
Bowser Inside Story (DS)
Golden Sun (GBA - DS)
Dofus (PC - MMO)
Wakfu (PC - MMO)
Paper Mario (N64 - NGC - Wii)
Final Fantasy Tactics (PSX)

Here's a thread I made of 100 good JRPGs. 

http://gamrconnect.vgchartz.com/thread.php?id=182989&page=1

EarthBound (since you don't have a Wii U, you would have to use an emulator)
Paper Mario & Paper Mario: The Thousand Year Door
Ni No Kuni
Bravely Default
Older Final Fantasies

Sorry if any of these have been said already.

Hmm you want JRPG and you dont have the KING of JRPGs the PS2? Get that before anything else and the Persona 3 and 4. And also I cant recommend The Lost Odyssey Strongly enough. Its not only one of the best JRPGs, its one of the best 360 games period.

He wants a good JRPG.  Not one so bad he'll despise the genre for years to come. 

I'm j/k, well, partially j/k.  Ni No Kuni isn't a good game though.  Although this is a reply to everyone who listed Ni No Kuni, and I noticed that everyone who listed this game also listed Valkyria Chronicles which is a good game, although less of an RPG and more strategy than anything.

Well, neither one is turn-based, which is what the OP is specifically asking for, so I don't get why the two are even mentioned.

Valkyria is a unique combination of turn based strategy with real time third person shooting/RPG stuff.