Congrats. Plenty of exclusives you will enjoy.
Great start with Mass Effect. Amazing story in that game. :)
I know you love FF and square. To be honest, none of the square games are as bad as people make out. And if your a square fan you can probably add another 8-10% to the review scores.
Get the following games in this order. Take out any games for genres you dont like.
Lost Odyssey (This game is very very good. It is Hironobu after all. You love FF, you'll love this very emotional)
Fable 2 (this is a must)
EDIT: Ninja Blade
EDIT: Ninja Gaiden 2
Gears Of War
Gears Of War 2
The Last Remnant (they have been patching the game)
Infinite Undiscovery
Dead Rising
Halo 1 (I know, I'm assuming you havent played the first one or second)
Halo 2
Halo 3
Blue Dragon
Forza 2
I'm sure you wont have loads of money to spare, but most of the games above are cheaper now.
Just enjoy your 360 and PS3. As long as you dont let any fanboy feelings get in the way you'll now have the ultimate setup. (the fact you paid out for an Elite kinda shows your no fanboy :) )