so do you suggest to start again from the beginning?
That'll depend on the content that's needed, honestly. In the last ~3 years there have only been 2 real updates, Aqua and Diane, which actually required any significant amount of old content. So for every other update, not counting 0.5 updates for Diane and Jenny, it didn't matter whether you had it in your save or not (as long as you played in the money/stats-cheat-mode, obviously) and you could just play the new content until the end. I'd personally expect the same to be the case for 0.20.
As said, your old savegame will likely work but there's probably an increased chance for bugs. I may of course be wrong with both of those predictions.
Edit: For 0.20.5 that's of course going to be different and one should use the 0.20.0 savegame to continue the story.