I'm not sure that paying zero tax now is the right goal.
I always thought that you wanted to have your marginal tax now about the same as your marginal tax when you were retired and removing money from your tax sheltered accounts. That way, you'd never be in the super-high marginal tax brackets. So the strategy might be called "fill up the reasonably low brackets", which, if you ask me, is at least the 15% bracket.
The advice I gave my kids was to get the 401k match, then put the rest in Roth, and to use a Roth 401k if you could. The asterisk was that if they ever started to make "a lot of money", which pushed them into the high tax brackets, then revisit the idea, and possibly put money into tIRA instead of Roth.