Images are a very important consideration for site speed, since loading larger-than-necessary images is a quick way to slow your site down. Ideally, your site should load the correct sized image for the screen it's being viewed on -- and that means compressing those images down.
You can compress your images before you upload, after you upload, or both. In the past, we recommended you do both in order to get the best performance. If you want to continue doing that, that's fine -- we recommend uploading photos at around 2,000 wide on the longest size.
However, our server-side optimization tools do a great job of compressing images, so it is no longer necessary to compress images before uploading them.
When WordPress receives an image for the first time, it generates a range of sizes (called thumbnails) that are pre-arranged by your theme or plugin author. Because of this, it's important to have a server-side compression tool. (Or you're only compressing the large image, not all the other sizes, which will load 80-90% of the time!)
There are several plugins that can be used to compress images after upload. The only tool we recommend for this is Kraken.io, and licensing for this is included on all standard Performance Foundry Managed Hosting plans. For 99% of people, choosing to process lossy (where the whole image is recompressed) is the best way; for some (photography sites, for example), lossless compression is best: it will strip metadata without impacting the image itself - giving the professional photographer more control over the image with the trade-off of a slower site.
One of the additional benefits of our Publisher and Publisher Plus hosting packages is additional image compression using Thumbor, which makes your site load even faster. It's great for image-heavy sites, especially blogs with lots of photos.