I am extremely DIY oriented and love to give friends and neighbors the confidence that yes, we can pull it off. With time and a little wisdom I have learned that this confidence can lead you astray. It has taught me a certain reluctance to any new project. Of course, this is after opening up a whole house full of hidden problems.
In this case, I would like to make the argument to not regrout your shower or daily use bathtub. The reason is the end result. (I just got done cleaning my shower, so I may be a little biased.) Even if you are the most die hard caretaker of grout, it will inevitably fail again.
A shower that is thankless bitch to keep looking new. If I could do it all over again and eventually I will be, I would send that 1970's tile straight back to hell. I will tear it down to studs and install a fiberglass surround. Indefinite low-maintenance.
I have personally been fortunate enough to live in several nice new houses with fiberglass surrounds and I never thought they looked bad or cheap. I acknowledge that fresh tile looks great and has a quality superlative to plastic, but it is a short run. So, keep the tilework in rarely used guest bathes to impress your once a year visitors.