Which is to say, I want a page that shows the content of "Your latest posts".
To understand what I mean by "You latest posts" go to:
Settings > Reading > Front page displays and one of the options is "Your latest posts".
A page needs a template, but rather than code it myself using the API (which I have done, albeit poorly) I would like to just use logic that is already existing, particularly with the pagination.
home.php
template, if available, to show the posts or it uses theindex.php
template - see in codex. So I would recommend to create ahome.php
template and make it fit your needs. Thats pretty much it, there is not really a lot more existing logic to use.