Just pick a wall, buy the faux brick and glue to existing wall leaving space for the grout/morter. The brick should have instructions on installation.
And make sure there are no leaks in the basement that will damage the new walls. Sounds challenging. How about taking photos and submitting your work to Hometalk? This could help a lot of people!
this is the one I did in my dining room: https://www.craftylittlegnome.com/real-thin-brick-accent-wall-tutorial/
Hi Kathy: Here is a site I found that doesn't really use the faux brick you can buy, but I found it to be fascinating and am going to try it in my basement. Give it a peek and see what you think: https://www.hometalk.com/34049335/faux-brick-wall-step-by-step-tutorial-for-under-30? Good luck