Hello all,
I am trying to put together a layout for the home page that would require the editor to insert code snippets that style some basic services based on a custom CSS class.

What I can't find a nice way to provide is a way for them to edit these snippets with the information about the service and an image and add them to the front page in a way that doesn't require them to know any coding at all. A good example is this bootstrap demo page that has the circle images and paragraphs under the carousel slider:
http://getbootstrap.com/examples/carousel/

I can't find a way to provide an interface for the user to add those headings.
Maybe a holder class that includes all the children of the home page? And each child page could contain the content of the headings?

Not sure how best to approach this in SilverStripe's framework.

If you're planning to have a view details link to the content like the example, then a child page for each sounds like a good plan.
If the blocks are only being displayed on the home page then having a class for the section and add it to the homepage with a has_many relationship and a gridfield in the cms might be better.

In your home page template you'll be looping through either the child pages or the objects, doesn't really matter which.

holder/children
https://www.silverstripe.org/learn/lessons/the-holderpage-pattern?ref=hub

Has many dataobject
https://www.silverstripe.org/learn/lessons/working-with-data-relationships-has-many?ref=hub