Seeing that we're more or less going along with Meyer's (minus the sparkling [s]because seriously I can never get over this bit it's just so ridiculous haha[/s]), we can have our characters to develop some sort of gifts - something subtle, not those really crazy stuffs you see in DC/Marvel heroes. We can even dab into the realms of possible ritual/dark magic depending on the IC development.

Sure - or if you want we can also make this RP some sort of a continuation from the book series but set apart from the canon events (basically borrowing concepts and some references but no direct canon links). Since the Volturi controls Europe or much of the vamps in the west, we can have another undead government that rules over the vamps in the east to maintain some sort of power balance, and this can be further developed into a clash between the two factions with our main characters as the center of the conflict.