I think I would do the CRC before the CDEO. I agree with the above response that AHIMA is the preferred certification and more well known for CDI. In my searching over the years I have also found most CDI roles are for those that have a clinical degree/license such as RN, BSN along with the coding certification(s). Depending on what certifications you may already have I would say the CRC would be more marketable right now.
I wouldn't base my choice of certification off of those "top paying credentials" lists. Don't forget, the folks that respond to the salary surveys in those top paying lists probably have other degrees, 20+ years of experience, and may be in management, supervisory or senior roles. I think some of that can just a marketing tactic for getting more people to take the courses.
CDEO could be a good tool for auditing but I would get the CPMA first if that's what direction you would want to go. That is more desired and employers know about it (in my experience). Unless you specifically want to try to obtain a role in CDI only.
I personally have never wasted my money on the "courses". I do the study guide and all the practice exams over and over until I get the practice tests down, then take the exam. I think it depends on your background, test taking style/ability, and level of prior knowledge. If someone is completely new and has never coded or had any knowledge of medical billing, claims, coding, insurance, medical terminology, etc. it's going to be really difficult to pass anything.