Using a pre-built CDN image transcoding solution
When transcoding images, you have two options: use a prebuilt solution, or make one.
Most CDN providers have services that will automatically resize images for you, to display them to your users, so that you don't have to code anything: you just add a query string to the URL, and then the CDN resizes according to that. For instance, you might enter "https://yourwebsite.com/image.jpg?width=640&height=480", and the CDN would resize the image to those dimensions and send the viewer that size.
This approach has advantages and disadvantages. For an art website, I would say the disadvantages heavily outweigh the advantages, and it is much better to transcode images yourself. A rundown of the factors to consider are below.
Advantages
Ease of deployment
Since you don't have to code anything, a prebuilt image transcoding solution makes it very easy to serve resized images without having to add any extra functionality or code to your site.
Generally not CDN-dependent
As most CDNs offer this service, or a similar one, you don't have to worry about being stuck with your current CDN provider if you choose to use a prebuilt solution, as any provider you move to will almost certainly have one as well.
Disadvantages
Lack of quality control
While you can in some cases control the output quality of images that are resized with a prebuilt solution, you rarely get full control. For instance, you may be able to change the quality setting, but not the chroma subsampling or output format settings, which are significant for an art website where chroma subsampling can degrade image quality and output formats do not have equal compatibility in artist software.
Potential for high costs if used incorrectly
The basic premise of most prebuilt image transcoding solutions through a CDN is that you give it the dimensions you want, and it resizes the image to those dimensions on the fly. Give it 640x480 and it gives you a 640x480 image... but what if you then give it 640x479, and 640x478, and so on?
It's possible to end up with a large number of unused resized images in your cloud storage, where an incorrect or unnecessary size was requested, that just sit in cloud storage buckets accumulating storage costs. You need to only request valid sizes, preferably by confiuguring your CDN solution to only use certain sizes or such like, and ensure you have proper lifecycle rules on your cloud storage buckets to delete old or unused resizes after a period of time.