I know very little about Babylonian History and would like to have a grasp on it. I want to know about Nebuchanezzer primarily but a general history could be interesting.
For a general history of the region I recommend A History of the Ancient Near East: ca 3000-323 BC by Marc van der Mieroop. I'm reading it currently after seeing it on the AskHistorians Book List and think it's a very thorough and accessible read on the topic. I can't recommend anything specifically on Nebuchadnezzar or Neo-Babylon, but this book does cover both of them.
Journal articles. Many of them are easy to follow and very interesting to read, especially after you've already gotten very familiar with the basics. A good place to start your search is JSTOR or Google Scholar.