UPDATE: Zeus and Isaac Clarke have joined the Battle Royale in Version 3.0!
While the official site does a great job in exploring the history and games associated with the roster, I kept wondering to myself: "But wait, WHEN did these characters debut and in what order?" So I took the liberty of making this timeline in Photoshop. Hopefully it serves as a nifty little reminder of who's the "oldest" and who's the "youngest." Props to you, Heihachi!
Heihachi: While the first Tekken actually appeared in the arcades in late 1994, this timeline counts its first appearance on an actual PlayStation platform: March 31, 1995.
Big Daddy: It is a widely known fact that BioShock did not debut on PlayStation 3 until over a year after its August 2007 debut on Xbox 360. But, unlike with Tekken, BioShock on that platform was essentially the same game as the PS3 version; it just happened to release much later. In essence, this timeline is not claiming that BioShock was released on PS3 in August 2007, but that Big Daddy first appeared in BioShock and has existed since August 2007.
Dante: Yes, Don'te/Dino/whatever you'd like to call him has the original Devil May Cry's release date. This is because this Dante is meant to represent both Devil May Cry series as a whole, and not just the 2013 reboot. Dante's official All-Stars page also acknowledges the original four Devil May Cry games, so this timeline will do so as well.
I'm impressed. KUDOS to you and for Heihachi as well, probably the most overlooked character right now. Legend.