Image Format
I believe the preferred performance is WebP. But I usually try to use png over jpg.
Compressing Images
I think what might work best in your case is some sort of plugin like WP Smush. If you have a ton of images I'd invest in a tool or plugin that dynamically compresses images as they are uploaded to your site.
I like WP Smush because it also strips out the metadata associated with images along with compressing them.
If you have a ton of images it could be an attractive solution for you that you can scale.
Outside of another plugin, you could try some sort of cloud-based solution to dynamically compress images before you upload them.
I've tested an open-source image compression tool called Caesium in the past. This tool reduced some of my images by almost 40%. It performed better than the plugins I was using but I'm not so sure it would be a scaleable solution for you.
Out of curiosity, how bad are your load times? Are you currently running into site speed problems or are you trying to make incremental improvements?