how to creating includable “new posts” on a different part of a website

I would use RSS and I like this plugin:
https://wp-plugins.net/index.php?id=88

Others are here:
https://wp-plugins.net/index.php?filter=rss&filter_search=Go…

In a totally different folder than my blog I just saved my file where I wanted to display the “recent posts” as whatever.php, then
put at the very top of it (before everything)
<?php
require('./path-to-your-blog/wp-blog-header.php');
?>
(which makes available all the WP functions on that page) and used the recent posts plugin.

Thanks very much everyone — I ended up using rssLinkList.php as suggested and it worked great. Since my main index file is a HTML with server side include enabled, I actually have to:
do:

<!--#include virtual="recent.php" -->

then create a recent.php file, which calls rssLinkList with the right arguments.