Migration Assistant

To complement RonasarA's post, you can select specific folders to migrate (see http://www.creativetechsupport.com/help/mac/transfer/migration/select.html). Yet, you won't be able to choose specific files, such as specific photos.

To do this, you would have to migrate only the things you mean to migrate and, using Time Machine, restore specific files.

Yes, you can select what items you want to transfer. Please see link at the top of this page: Move your content to a new Mac

If I remember correctly, while you do have some options as to what to transfer, when you select to transfer your files, there is no option to individualize what to transfer. It's all or none. You can transfer apps or not and your preferences and settings or not. Your operating system is not transferred. I hope this helpful.