Logging user in with PHP

Hi, everyone. I’ve been doing some research on how to log a user in using PHP. Here’s what I have:

if ( isset( $_POST[ "nome_de_usuario_ou_email" ] ) && isset( $_POST[ "senha" ] ) )
{
    if ( username_exists( $_POST[ "nome_de_usuario_ou_email" ] ) || email_exists( $_POST[ "nome_de_usuario_ou_email" ] ) )
    {
        $credentials = array(
            'user_login'    => $_POST[ "nome_de_usuario_ou_email" ],
            'user_password' => $_POST[ "senha" ],
            'remember'      => true
        );

        $check = wp_authenticate_username_password( NULL, $_POST[ "nome_de_usuario_ou_email" ], $_POST[ "senha" ] );

        if ( is_wp_error( $check ) )
        {
            echo "<p>As credenciais fornecidas n&atilde;o est&atilde;o cadastradas.</p>";
        }
        else
        {
            $user = wp_signon( $credentials, false );

            wp_set_auth_cookie( $user->ID );

            /* Displays pricing table: */
            wp_redirect( "http://sellerconnect.com.br/index.php/precos/" );
        }
    }
    else
    {
        echo "<p>As credenciais fornecidas n&atilde;o est&atilde;o cadastradas.</p>";
    }
}

This isn’t working, though. I’m kind of confused on which functions to use. For example, should I use wp_set_current_user instead?

Thanks in advance!