The way I’d approach that is to have all posts you want on the homepage assigned to a category called “Homepage”, and modify the template file that displays your home page (usually index.php but can vary by theme) so it only includes posts from that category when displaying the home page.
this code goes before the WP loop, if the category id for the homepage category is 5:
if (is_front_page() ) {
$paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
query_posts("cat=5&paged=$paged");
}
The unresolved issue so far, I believe, is that you want only admins to be able to assign a post to that homepage category. If all your authors are cooperative and trustworthy, they just don’t use that category and all will be well.
If you don’t trust the authors in that way, then you need something that prevents any unauthorized author from assigning the homepage category to their posts. That would be a plugin. This is a failry common request on the forum and not sure the great plugin that accomplishes this has been created yet.
I did not do a complete search of the plugin directory, but in a few minutes came up with this one.
https://www.ads-software.com/extend/plugins/admin-only-category/
If the idea seems workable to you, you could try that plugin out, or search the directory for a more complete one. The gist is, it would hide the existence of the homepage category from anyone who is not authorized to put a post on the homepage, so their posts could not appear on the homepage after you add the query_posts code I pasted in above.