I created a page that I want to use as my home page for the site. 

Without having to redirect to this page, is there a setting in the ACP where I can say that I want this page to be the index.php essentially so that when user visits domain.com, they are shown this page?

If not, what other ways are people handeling this with their "Home Pages"?

under applications just star pages

You also need to select one of your pages as being the default in Pages. On the screen where you can create and edit pages, bring up the options for that particular page (downward arrow) and choose "set as default".