How to login and contribute to a wp blog from another app

I use WP as a CMS which provides content to another app i have developped.
The user logins in my app with a username and password.
I would like that, when the user logins in my app, he is automatically logged into WP and can use the WP site as he was logged from the standard WP login form.
I have seen functions wp_create_user and wp_update_user, so I feel comfortable with creating or updating WP users from my app.
I have seen the functions wp_signon, wp_authenticate, wp_getuserinfo and wp_logout, which looks lile a good starting point for login and logout user.
But i have also seen lots of posts on the web from people who used wp_signon, but says the user was signed on but not exactly as if they were logged from the standard WP login form. Some people says for instance that, as soon as the user moves to another page, he is no longer logged.
So which functions do I have to use to login the user exactly as he has logged through the standard WP login form, including the creation of WP cookies?
Thanks in advance for advice or even sample code.