Hey Mike,
Looking at your root landing page, there's lots of opportunity for improvement. Before you tackle image optimization or any of the other suggestions, I would suggest doing some clean-up of the page. It appears you have a large number of unused assets (images, JS files, etc) that are negatively affecting your pageload. Remember, everything that gets included on the page is something that the client will have to download. The more files (and larger they are), the longer the page will take to load.
Webpagetest.org is a good place to see all the assets being included in your page. Here's an example I ran for your main page:
https://www.webpagetest.org/result/180116_CG_a121069ce19f27a0393370db09f9703d/3/details/#waterfall_view_step1 I wouldn't focus too much on your PSI (pagespeed insights) score until the clean up is done. After that, you can come back to this tool and run it again. Within the pagespeed insights errors, there are notes on how you can go about fixing them. For example, under "Optimize Images" there's a link with some good information in it:
https://developers.google.com/speed/docs/insights/OptimizeImagesGood luck, Mike!
-Ian