Could I patent an idea to make something better than it currently is?

It sounds like your idea would fall under copyright protection, rather than patent protection. But both copyright and patent protect the specific expression of an idea, not the idea itself. So you can create a web site that sells textbook just as this other company has. However, you couldn't copy the look and layout of the website or use a similar name.

In response to your first question - yes, you can sometimes patent an invention that makes something better than it currently is. Section 101 of the Patent Law says: 35 U.S.C. 101 Inventions patentable. Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title. However, the new invention must not be obvious to persons having ordinary skill in the field of the invention. Also, under current case law - inventions involving websites are often rejected as involving "an abstract idea" - which is not patentable. Go visit with a patent attorney to discuss your proposed invention. Be ready to discuss how you would make the website better.