I will be using an image from Adobe Stock on my book cover, but wanted to ensure that this is an appropriate use of a free image on the website. Please let me know any rules or stipulations when using photos from Adobe Stock for business purposes!
Free stock images can be used as stipulated in the licensing terms, also for business use.
Look here for more information on licensing: https://community.adobe.com/t5/stock/links-for-licensing-terms/td-p/11366788
(Disclaimer: As always with licensing, this is my interpretation of the rules. I think they are correct and advice is based on reading and interpreting the licence terms and on fair use for both the buyer and the artist/stock company, but I cannot rule out that my interpretation is wrong. I'm not an Adobe employee).
I cannot comment on the licensing aspect of your question but you may want to consider if it is a free asset that you run the risk of seeing the image elsewhere. No stock image is exclusive, that's the nature of it being a stock image, but free image has the possibility or risk of being used by others in various forms. A paid stock image is slightly less likely and paying someone to create an image that only you can use for your purpose is more costly but can be made to be yours to use exclusively.
Thanks for the link, this is helpful. In the Standard License description, it says that an image is free to use in up to 500k copies of printed materials, so if I used an image on a book cover that would be resold, would I be staying in line with the terms of a Standard License? If not, how do I go about gaining a copy of that image so that it is appropriate to use for the purpose of resale? Are there certain images that are not available to buy in an extended license format so that I can use them for resale products?
Either you need a standard or an extended licence. The licence type you need is depending on conditions that are described in the licensing terms.