Post feeds on main page (home.php)?

Not sure if there’s a plugin for this, but I’m hoping someone can find a way to help out here.

https://www.considering-gastric-bypass.com

This is the testing ground for a client’s site I’m doing, but what we’re looking to do is try to have a static “home page” (which was accomplished with home.php) but be able to somehow use a “teaser” plugin on that page to feature certain posts, depending on various reasons, but having nothing to do with how recent they are or what category they’re in.

The reason for the static “home page” is because we didn’t want the whole scrolling posts thing… and just because we make a post sticky in one category, we don’t necessarily want it sticky on the index page.

Short of hard-coding the links in, I’m at a loss here. Is there any type of plugin instead of “adhesive” or some other “sticky” That we can use to pull in posts based on a tick box or something?

Again, just because something’s on the “home” page, doesn’t mean we want it sticky on it’s own category page, and vice versa…

Thanks in advance for any help on this… I tried searching but don’t think I’m using the right words for my search…