As someone who was in test for 13 years and has transitioned to information security in the last 2 years, I've thought long and hard about all of this.
First, as others have already said, certifications don't matter that much for most organizations. Some industries will require them because they have little else to use for verification of knowledge/skills. Mainly government and large highly regulated orgs like banks or insurance. Which is the same for test related certs as well. They're only as valuable as the person(s) reviewing your resume.
Second, is showing your own initiative to learn. This carries quite far in infosec. The courses that support the certs will help to show that, but security is very broad and very deep at the same time. There are some sub-genres, but they all intersect to some degree. This means you need to be always learning and always researching.
All that being said, the CEH course work is not regarded terribly highly. Many are drawn to it because it says "hacker" in the title, but depending on where you are in your career it may or may not be worthwhile. Since you are just starting though, it may help you to figure that out and show what you do or don't know and figure out how you want to move forward. Especially if someone else, like your employer, will pay for it :)
Also, there are a lot of great resources to find out how you want to pursue your new career options. Thankfully there are folks out there like @mubix who have been kind enough to compile a lot of those resources in one place. Check out his gist on github here: https://gist.github.com/mubix/5737a066c8845d25721ec4bf3139fd31
Hope this helps! Don't be intimidated by all the data out there, everyone starts somewhere :)