I like Annaliese better.
Anna is used so often and I've heard it so much that I find it extremely boring. It strikes me as a filler name that people use when they can't think up something more interesting.
Annaliese, though I prefer it spelled
Annalise, I find to be much prettier and more interesting to look at and say. I also like the similar names
Annabeth and
Annalena, for the same reasons.
For a middle name combo, I like
Kaia the best. When paired with Annali(e)se,
Christa causes a hissing double S sound.
Lara is okay, but I think
Kaia flows the best.
Hope I helped!