Note this is a snippet from a class, you can replace the $this-> with your params or hardcode them. Its all ran during admin_init.

welcome.php

<?php

/**
 * Sends user to the start page on first activation, as well as each time the
 * plugin is upgraded to a new version
 *
 * @access public
 * @since 1.1
 * @return void
 */
public function welcome_init(){

    // Bail if no activation redirect
    if ( ! get_transient( '_' . $this->plugin_slug . '_activation_redirect' ) )
        return;

    // Delete the redirect transient
    delete_transient( '_' . $this->plugin_slug . '_activation_redirect' );

    // Bail if activating from network, or bulk
    if ( is_network_admin() || isset( $_GET['activate-multi'] ) )
        return;

    if( ! $this->upgraded_from ){ // First time install
        wp_safe_redirect( admin_url( 'index.php?page=' . $this->start_slug ) ); exit;
    } else { // Update
        wp_safe_redirect( admin_url( 'index.php?page=' . $this->update_slug ) ); exit;
    }
}

Note version numbers can be handled to your liking, this is how I do it: https://gist.github.com/zanematthew/f8440442df8524a9dff0