What platform would be the best for a family history website?

My cousin is building our family tree and gathering history. She is using a very basic website that lets you just plug in text and pictures. It’s not searchable and apparently not indexed by Google. I want to build on my own domain and import her data to a more current format. I do not want to build my site within Ancestry.com or ourfamily.com

I’m looking for a software platform that would best suited to displaying family history information while allowing me to connect family members information and maintain their family line, for example by creating categories starting with the first member of the family she has been able to identify and then nesting inside that category. So if you wanted to look up your grandfather and be able to see other members of your branch of the family it would be easy to follow based on the category.

Blogging software is the easiest that comes to mind and if I go that route I will use b2evolution but maybe there is something else out there that is intended for this type of site and has a sql database on the backend.