I think Chrono Trigger is a great game to start off with. It's not extremely difficult, doesn't have a difficult learning curve and is well designed even by todays standards. it's also considered one of the best RPG's ever.

I don't suggest playing the DS FF 3 or FF 4 because they are kind of difficult and if you are a first timer to RPG's it might be more frustrating than fun.

For you second RPG if you are a fan of story then check out Xenogears (which was made by quite a few people from the Chrono Trigger staff, also there is actually a but load of reading in that game so that might not appeal to you) or try the Xenosaga series (which has voice actors).

Hoo boy.

Try Final Fantasy IV DS or the DS port of Chrono Trigger.

FFIV was my first Final Fantasy, pretty much my first hardcore JRPG, and it is about as good as they come.

An rpg u shouldnt miss out is Final fantasy VII.

Hmm?  Oh, sorry.  I think we must have had a communications breakdown...

Seconded

Oh God

Now there's going to be a fight

It's okay, you two, we will stand together for FFIV - a more elegant game for a more civilized age

Final Fantasy 4 (DS) is a great start. It's a bit difficult at first, but much easier than 3. It also is a good start into the series, since it does have a cool story and the overall FF feel, but is also a more traditional fantasy RPG (later FF's have lots of futuristic influences).

On Wii maybe try the GC games Tales of Symphonia or Skies of Arcadia. Symphonia 2 (Wii) might be ok as well, but I recommend starting with the first. The VC game Secret of Mana is also a very good start.

PS2 there's loads. Maybe try some PS1 classics first like FF7, Xenogears and Suikoden. PS2: FF10 is a great game. Suikoden series, Dragon Quest 8...

FF12 on the PS2 is a fantastic game but I don't recommend playing it first. It will completely ruin you to JRPGs, either because you will hate it or because you will love it so much that other JRPGs seem pooey in comparison.

The first RPG I ever played was the original Dragon's Quest (Dragon Warrior here) on the NES.

I would say the first game that really got me hooked though was Final Fantasy VI on the SNES. There is a remake of that game you can play on the DS so I would look into that one first.

There have been lots of good PS1/PS2 suggestions in this thread already so I'll skip those but for X360 I would try Tales of Vesperia and Lost Odyssey.  I would skip the rest on the system since you already have a full plate of classic games to play.

Kingdom Hearts!!!!