There's a variety of myths about starting sentences with conjunctions. The best explanation I've heard from these myths is that they started with prohibitions from English teachers to stop pupils writing entire pieces where every sentence did so ("And then I went to the park. And then my friend came and we played together. And then we went home. And then I had my dinner.") that was taken to be an actual rule. It's not.
Would "Now ......" be enough?
Well, it might. Depending on the rest of the sentence, this might not only be acceptable, but also make for a stronger sentence - whereas can be a rather weak word sometimes. If the opposition of past and present is clear, then I would certainly consider starting just with Now.
Both would be correct though, so it's not a matter of the "right" choice, but of the strongest.