I don't do technical writing. I just write articles.
However, I do constantly have the following books on my desk:
The only one I ever really use is Elements of Style.
I did thumb through 'Technical Writing for Dummies' a few years back. It actually seemed pretty decent if you don't have experience with technical writing. All of the 'For Dummies' books are decent books for those getting started with specific writing styles. For example, the following acted as decent starter guides for a few projects I worked on:
So, since you said that you are brand new to technical writing, I do suggest that you pick up 'Technical Writing for Dummies'. Can probably get it for a couple of quid used.
https://www.amazon.co.uk/Technical-Writing-Dummies-Sheryl-Lindsell-Roberts/dp/0764553089
Elements of Style is a 'must have' for any writing, though.
As I said, technical writing is a whole different ballgame to what I am used to. I would never touch technical writing, so I have no idea how useful those books will be.