"How do I add posts to my other page without them showing up on my static homepage?"
This would be very easy to do. But the blog front on fifty5centsbookblog.wordpress.com isn't a static page at all, it's the special showcase template page of Oxygen: a dynamic page that displays your latest posts (in two sections).
In practically every other theme you wouldn't be able to exclude specific posts from showing on your latest posts page. But in Oxygen is possible, because if you set a recent post as a sticky it will disappear from these sections (since it should show in the slider), but it won't show in the slider if its featured image isn't wide enough.
Oxygen requires featured images that are at least 470px wide, but the slider requires featured images that are at least 750px wide. So the solution is: create a "Weekly meme" category, add it to your custom menu, file these posts under this category, mark them as stickies, and set a featured image that is 470px wide or wider but narrower than 750px.