Lots of images size in wp-content/uploads how to delete some

Hi everyone,

First time I'm publishing here !

I have a big problem I have pushed aside for a while but I need to solved that once and for all.

I've used several wordpress themes before creating my own using genesis.
The problem is, when I started, the first theme I used was crap and it created lots and lots of image sizes. So my wp-content/uploads is loaded with many images which ends in having a wp-content/uploads very heavy.
In consequences my backups are heavy too and most of the time it causes problems when I want to automate backups.

I would like to get rid of most of the image sizes but I don't how to delete them and which one to keep or delete.

I've joined screenshots of what I get when I started my site (sizes-1) and what it looks like now I have my new theme. (sizes-2)

I've tried to use smush.it plugin on a test version of my site but it didn't want to work. I have an error message.

What can I do?