I own The 3rd Birthday, but I've yet to play it (busy with other games). I'll get around to it eventually... "eventually" as in maybe a few years from now, but from what I hear, there's a good chance the first game will still be my favorite in the series.
As for the Chrono games, you can't touch Trigger; that game is too much of a timeless classic, and the fact it was ported to the 3DS and people still bought it shows that the game has stood the test of time. Chrono Cross is also a good game. Not as memorable or as beloved as Trigger, but it's still solid. Yes, the characters are different and there's pretty much nothing in the way of tying the two games together, but isn't that what Final Fantasy was as well? Final Fantasy II was nothing like the first one in story, world or characters, and that became a tradition in the series, with the only things becoming recognizable are things like the Victory Fanfare, Chocobos, Tonberries, etc.. Who's to say the Chrono series never intended to do that with their games?
As for other Square IPs - namely, the Mana series - they ought to just give the series a rest. Final Fantasy Adventure (Seiken Densetsu), Secret of Mana, Seiken Densetsu 3, Legend of Mana, and Sword of Mana were great and solid games, but then they wanted to make more and more which resulted in games like Dawn of Mana, Heroes of Mana, and Children of Mana, which were not well-received and generated mediocre sales. And yes, I've played them, and they weren't really great, Children of Mana in particular being very repetitive and boring. If they're going to make another Mana game, they really need to do it right, but with how far along gaming has come, fresh ideas are harder to come by.