Image on first post only

My website is http://boakandbailey.com, running WP 4.0 with a more-or-less out of the box Twenty Fourteen theme.

I would like the homepage to display as it is, with the same spacing and formatting &c., except without an image displaying for any post after the first.

This feels as if it ought to be easy, but I have struggled to implement any of the proposed solutions I’ve found online (counters and so on) because I’m not clear exactly where, and in which files, to make edits, or how one file calls upon another.

Is there a really simple, idiot-proof way of achieving this?

Thanks in advance for any advice you might be able to offer.

NB. I am using a child theme.