This is a great question, and one that's important to consider, since incorrect image sizing is the cause of most blurry images and slow image loading on websites.
In the past, it was good practice to upload photos of the exact size you'd be displaying -- but things have changed. Now, for most sites, it's unnecessary to use the "pixel perfect" approach. Instead upload your images with a future-proof width.
As rule of thumb, we recommend uploading your images at 2,000-2,500px wide, which will be full retina on viewing areas on screen areas up to 1000-1250px wide.
This is because, since version 4.4, WordPress has responsive images built in. This means that WordPress creates and displays smaller copies of the image according to your current theme and layouts.
Not in most cases. WordPress has had support for responsive images since 4.4 (December 2015), and almost all themes and plugins now leverage that. Only extremely out-of-date themes will need additional help from a plugin.
A qualified 'yes'. Larger images have a bigger file size, and that takes more time to transfer from the server to the user's browser. This will definitely show up in the majority of automatic tests that you run against your site.
However, the browser is responsible for downloading the best image size for its screen, so as long as you have a good range of image sizes available in the srcset, it should be able to make a good choice for both performance and display for your real users.
If you're of a technical mind, Smashing Mag has a good jumping off point. If you just want to understand how it works, read on!
The introduction of retina screens in high end phones and laptops meant a dramatic change in how images and text were rendered. Basically how they work is to 'squish' images into a smaller space to give the appearance of more depth and sharpness. It's a 2:1 ratio.
So the rule of thumb is to have images that are twice the size of the space that you're trying to fill.
Performance Foundry does a lot of that work for you behind the scenes: tools like Kraken, which run on upload; our Content Delivery Network; our on-the-fly optimisations for Publisher clients; and our special object storage all help to optimise and accelerate image delivery. If you'd like us to check your site, please email support.