Okay, I'm a massive dork and decided to research this.
The term "fair use" is not the correct one, it refers to reproducing parts of a copyrighted piece for education, criticism, etc.
Most of our work falls under "Derivative Works," which means we are altering the original to create a new work. It depends on what you do with your finished work, what effect it will have on the original, and how much of the original you used.
If it is public domain, as long as you put some creative effort into it, it's yours to play with.
If the copyright is still good (until 70 years after the artist dies), it gets tricky.
The basic guidelines seem to be that you must alter the work to use it (you can't just print/cut out a photo and call it your ATC). It can not be damaging, or infringing on the originals ability to make their own derivative works. For example, if Disney decides to make their own ATCs, or even if they think they might possibly want to some time in the very distance future, they can sue anyone who uses their images in ATCs. Extreme example, I know. Just buying a book of images does not seem to give you the right to use them. You need to buy or get permission per image, I believe.
Now if this makes sense to anyone, I'll be amazed. I'm not sure if I even understand all of this.
Claustrophilia - Based on what I read, altering the paintings is fine, however it is the postcard company that owns those specific prints of the paintings. I believe that since you (or your mom) bought the postcards they are yours to use, under the "first sale" rule. You cannot, however, reproduce the images. Although, I believe that means you can only use each image once, they probably didn't have transfer techniques in mind when they wrote that law. Silly judges for not realizing that you need the image to be printed in toner ink.
Here is one site that I got great information from and has a good FAQ about derivative works: Chilling Effects Clearinghouse: Derivative Works. They have a lot more information, I just wanted to keep to the original question.
ArtLex Art Dictionary has basic information and several links to other sites about copyright.
10 Big Myths about Copyright does say that infringement is infringement whether you sell it or not. (sorry ladies!)
Disclaimer: I am NOT affiliated with the law in anyway. In fact the closest I get to the law is that one day I'll probably be arrested and/or sued for breaking it.
Wow, I'm even more of a dork than I thought. Now that I've researched all of this, I'm going to continue to make ATCs that break almost every law.