For any very long time, I've looked for any wordpress plugin which will remove posts which are on the certain 'age' (eg. thirty days old). What's the easiest method to do that?

Here's some SQL which will find every publish that's been around for thirty days or even more:

SELECT * FROM `wp_posts`
WHERE `post_type` = 'post'
AND DATEDIFF(NOW(), `post_date`) > 30

To remove all of the posts, you are able to replace SELECT * FROM with DELETE FROM — but make certain you are taking a backup before you decide to do that!

After that you can just cron that any way you like, be that the spend script, a PHP script, or whatever you are preferred with.

Try the Auto Delete Posts plugin. Posts will auto-remove following the expiration date is hit