Images should be sized to the maximum required for internet use. Any digital camera, including modern phones will typically provide images with densities that allow high resolution printing or projection. This is far too big for website use. The pixels on our screens will render high quality display at much lower densities.
To put this in perspective, a modern mobile phone or good camera photo will be about 5,000 pixels wide and take up about 5MB of storage. If you load this on a website, every image you want to display will take up a lot of disk space and will take several seconds to download over the internet. The images have to be compressed and resized for web use.
A large 19″ screen is about 1,700 pixels wide. A laptop is about 1,200 pixels wide.
If you plan to display a large JPG image (full width on a large display screen) it needs to be resized to 1,700 pixel width. Along with basic compression this will reduce the size of a photo from 5MB to around 300K or 6% of the original storage space and bandwidth. Reducing the width further to the size that you need for inclusion in columns or blog posts will have a further exponential saving. (height and width will be less, so the saving factor is 4x)
PNG images can be even more resource intensive than JPG images, so PNG should only be used for smaller, simpler images or when transparency is needed.
Over the past few years the WEBP format was developed for internet use to offer a better solution to both JPG and PNG images. By now all browser support WEBP. It is even more compressed than optimized JPG images and PNG images, so for optimal performance, this should be used, where possible.
There are free online tools available to do image compression and resizing but they are cumbersome to use, especially if you have many images to manipulate. Programs like Adobe Photoshop do a fair job, but they are expensive and there are even better solutions available.
Fortunately there are several WordPress plugins available to do most of the heavy lifting for image optimization.