There have been many questions about image size and customizing images to fit a website.
Canva is a good place to customize your images quickly for headers, sidebars and featured images on your website. It also makes it easy to adjust or modify images to share on social media and size them to optimize them for the specific Social sites like Facebook, Google+ and Twitter. Each has an optimal size for their platform.
This tutorial gives a quick overview of how to create an image for the header image on your site.
The Demo site that I am using, uses the Twenty Thirteen theme. This is a pretty good theme but has a seriously UGLY header image. This is a good candidate to have the image replaced.
I hope that this tutorial opens up the possibilities for you. Canva is very easy to use, has many free images that you can use. There are images that have a price attached, most are $1 for access if you choose to use the paid images. Many images are free or you can upload your own images as I have done.
If you have an image that has a large file size, Canva will optimize the file size of the images for your website. This is an important feature as large image files will slow down your site load and is probably the most frequent problem that people encounter with their sites.