Create a blog within website

[themamazine]

My blog is currently set up like this
livelaughstudios.com/category/give or
livelaughstudios.com/category/pray etc.

I would like blog posts to be found at livelaughstudios.com/blog
and / or
livelaughstudios.com/blog/category/give or
livelaughstudios.com/blog/category/pray etc.

I would like the word blog to come first so that when people arrive to my website they have the option to choose my photography page at

livelaughstudios.com/photography
or my blog page located at
livelaughstudios.com/blog

Is this something you could answer for me or is it something I would need to ask in the wordpress forums?

Hope all that makes sense. Thanks for reading!