Happeo is designed to be responsive no matter which size screen you're working with. This means that you cannot fully control how the end user sees the image you've added to Happeo - how it looks depends on if they are on their phones, tablets or desktop computers.
That said, our recommendations for the image sizes are:
Logo in the Happeo toolbar: 140 x 26px
Splash image: 1200 x 1400px
Pages header (hero) images: 1920-1024 x 400px
Pages background images: 1920-1024 x 1080-768px
Channel header (hero) images: 1920-1024 x 315px
Images that are added to Posts and Comments can be any size as Happeo will resize them to ensure that they fit correctly.