A. I myself pronounce it /reg/ that is, so it rhymes with 'egg'. I do this for three reasons. Firstly, when I was a kid, I learnt the alphabet in a phonemic way, /æ/ /b/ /k/ /d/ /e/ /f/ and so on. Secondly, I work in Spain and here most people would automatically tend to pronounce the word like this even without knowing what it meant as there is a higher letter-sound correspondence than in English. Thirdly, in the past I have actually heard one of my very young learners mispronounce 'red' this way. This is also the pronunciation I shall use later on when I eventually come to putting audio with the stories.
However, in many countries where English is spoken as a native language, 'Reg' pronounced /redʒ/, so it rhymes with 'edge', is a short form of the man's name 'Reginald'. Therefore some teachers might naturally pronounce it this way.
The technique of using minimal contrastive pairs (changing one sound in a word to create a 'red herring' name that can then be contrasted with the correct pronunciation of the target word) can be used with either /reg/ or /redʒ/ as they are both just one sound away from the correct pronunciation of 'red'. So in the end it doesn't really matter. If you've started using /redʒ/ and you're happy with it, then that's fine too!