Create a wordpress admin user and only let them edit and post blog posts?

By “admin user” I’m guessing you mean someone who can log into the backend. If so, yes, you can go to Users > Add New in the backend, and create a user with the “Role” dropdown set to “Author”.

Adding an "author" user.

This person will be able to delete, edit, and publish posts, as well as upload files (e.g. pictures). See http://codex.wordpress.org/Roles_and_Capabilities#Author for more information.

If you need a user role with more limited capabilities (e.g. can only edit and publish posts, can’t delete them), use a plugin like http://wordpress.org/plugins/user-role-editor/ to edit the user roles.