What is the recommended size for the featured image?

The featured images at Mono occupy the full width of the site container, which is 1500px. The height of the featured image will actually depend on the height that the post title, post meta and subtitle occupy.

For the demo we use images with dimensions of about 1500 x 800 pixels. 

In any case, if you use large sized images, we recommend an image optimizer web app which is free to use and provides great results:  http://kraken.io
We just like using it ourselves, we are in no way affiliated to them, feel free to give it a try, they have a free optimizer.