Newbie question. Login/Registration. New PHP page

WordPress Core provides a lot of helper functions to accomplish these types of tasks. If it’s not a function, then there most often is a filter or action that you can hook into.

In the case of the WordPress login form, it’s wp_login_form(). Here documentation on that:
https://codex.wordpress.org/Function_Reference/wp_login_form

Regarding redirecting users after login, there’s a filter for that. This code is a snippet I’ve used on many sites:

function wip_login_redirect( $url, $request, $user ){
 $slug = $_SERVER["REQUEST_URI"];
 $islogin = strpos($slug, 'log-in');

 if( $user && is_object( $user ) && is_a( $user, 'WP_User' ) ) {

 if(($user->has_cap('edit_users')) && ($islogin==true)) {
 $url = admin_url('index.php');
 } elseif ((!$user->has_cap('edit_users')) && ($islogin==true)) { 
 $url = home_url();
 } else {
 $url = $slug;
 }
 }
 return $url;
}

add_filter('login_redirect', 'wip_login_redirect', 10, 3 );

I go into detail about that in this article:
https://wordimpress.com/conditional-custom-login-redirects-wordpress/

Hope that gets you going in the right direction.

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