Clear Varnish Cache (and maybe Views?) for Home Page when new story posted
Install the varnish module and set the minimum cache lifetime to none at admin/config/development/performance Also be sure to add the tweaks to the settings.php from the varnish module page.

This should ensure that the cache is flushed when new content is added.  You may want things to be a little more granular (if a complete cache clear at every content update would overload your server and cause performance problems) so using here are some other steps you can take: 

I found a nice article about using varnish which you might consider checking out.

The author recommends:


Go to the Varnish settings page (admin/config/development/varnish) and select "None" under "Varnish Cache Clearing". This will make sure that all pages are not flushed when content is altered.

Enable the Cache actions and the Rules UI module
Go to Administration => Workflow => Rules and click "Create a new rule"
Select "After updating existing content" under "Node" as the reacting event
Add the "Clear a specific cache cid" action
Select cache_page as your cache bin.
Put "node/[node:nid]" in the value text area.



Try to edit one of your nodes, everything should still work. The difference now is that we are actually only purging the entry of the particular node that has been edited not the whole page. You can try this by visiting another node, notice that it is still cached by looking at the Varnish headers. 

You will probably also want to clear the views cache (for your relevant views) so they are updated instantly.  Testing should be relatively easy by adding new content in a browser and refreshing another browser window that isn't logged in.  You should see your new content appear immediately at refresh.