A bit more information about .COM vs/ .ORG
https://en.support.wordpress.com/com-vs-org/
You can create “thumbnail galleries” where WordPress takes many photos and captions and organizes them into a grid and displays small pictures and then click on a small picture for a larger view – standard feature – there are also “Plug-in’s” that can help arrange and display pictures and some “Themes” are designed help you make a Photo-blog if most of your family stuff is pictures.
The thing to remember is that blogs are a tool for you to give out information on the web – WordPress is a tool to help you make a blog – many times we get too wrapped up in the “tool” and loose track of what we intended to do –
My suggestion is to make a list of what you want to do and what type of information you will be sharing (stories, pictures, etc) before you go very far –
If you have more questions ask them here or at WordPress.com – both places have very helpful people that can help you go in the direction you and your family want –
The WordPress software is very flexible so you can change your mind down the road as your story develops.