First set up your new WordPress site with all the menu’s and categories you desire.
Secondly: export your content using the backend of your blogspot account. Make sure you have a copy of all the images as well on your harddrive.
Import the posts into WP and assign them to the correct menu’s. Each post’s image(s) will have to be put manually into the post. An alternative is to leave your blogspot page alive so the images can still be read off your current site into the new WordPress. But be carefull. Closing your blogspot will remove the images on all your posts on the new server.