There are a few things you can do to optimize images so they load faster and are optimized for your visitors. I will not try to explain all the options, as there are some great posts explaining the benefits of each plugin, like this post about the 10 best image optimizer plugins for WordPress. With all of those plugins, you don’t need to have Photoshop or other image editing software to reap the benefits, but of all the plugins I read, the resulting optimized image would be stored on the host server where your instance of WordPress lives.

If you really want to speed up image load times for users all around the world, the next step in your need for speed would be using something called a CDN (Content Delivery Network). In short, it is a way of having all your images stored on servers around the world, so anytime a user in another part of the world wants to see a picture, that picture does not have to travel as far and transfers quicker. Here is a rundown of CDN plugins/services that work with WordPress.

You asked specifically about the best image size for your users, and I wanted to point out Hammy from the list of top 10 above as an option.

Hammy takes your regular content images (only within posts and pages, not custom post types) and regenerates a number of smaller sized images. When a person visits your website, it then automatically provides them with the most appropriate image (or the smallest one possible). This makes for a better experience, especially on mobile.

Using Hammy you would not have to choose which size, but would allow the device your users visit your site to dictate what image size they see (and image file size downloaded).

Happy Blogging!