I love the name Susanna/h, it's gorgeous. So many short forms that can be used eg Susie, Sukie, Zanna etc. It's a name that is classic and has never been overwhelmingly popular, so it cannot be tied to a particular generation imo. Whereas Susan, which is a variation of the same name, was so popular in the 50s and 60s that it is considered an older middle aged woman's name, and will probably take 20 years to come back. I actually like Susan too, but Susannah is more beautiful. As for the 'h' on the end, I can never decide which version I like more, about the same I think. Susanna with no 'h' is the version used in continental Europe I believe, if that makes any difference. I do think that it is better with an 's' in the middle rather than 'z', just looks more pleasing written down imo.
And it has a completely different vibe to Savannah, even though it sounds quite similar. Savannah edges towards tacky (even though one of the late Queen's great grandchildren is Savannah!). Savannah also wouldn't have the same short forms.
I do really like Laura too, it's also classic, but due to a surge of popularity in the 80s, it is a bit more tied to the generation now in their thirties.
You could also go for Anna, Katherine, Emma, Elizabeth, Zoe, Christina, Helen or Helena all pretty classic timeless names.