How to make sure people will see all the items/options on my website?

I'm designing a website for a dog and cat shelter. We will put the photos with the descriptions of the animals and any other useful infos.

Since there are about 50 dogs and 100+ cats, how can I make sure all the animals will have equal chances to be seen? I could periodically change the order in which they are written in the HTML but that would be way too much work and I couldn't keep up with this practice.

Is there any best practice for this type of case?

Thanks you very much!