Definitely Olivia! I love this name (my second favorite girls' name), and Alivia, though not terrible, doesn't do much for me. It's not the worst spelling out there, but Olivia seems so much more classy and traditional. Middle name suggestions:
Olivia Rachel
Olivia Rose
Olivia Katherine
Olivia Marie
Olivia Grace
Olivia Hope
Olivia Margaret
Olivia Audrey
Olivia Brooke
Olivia Brooklyn
Olivia Caroline
Olivia Celeste
Olivia Christine
Olivia Camille
Olivia Faith
Olivia Jasmine
Olivia Jacqueline
Olivia Michelle
Olivia Megan
Olivia Nicole
Olivia Natalie
Olivia Payton
Olivia Raine
Olivia Taylor
Olivia Josephine
Olivia Juliet
Olivia Iris