You can get the latest version (0.5.1) and start right away.
We did a pretty extensive code revamp last year so if you have any saves previous to 0.4.1, I recommend not to load them and to start from a new save and use the skip button to get to where you were. You will experience so many bugs the game will be basically unplayable.
I also highly recommend keeping a save file handy at the start of chapter 14 (and this goes to everyone reading). The next couple updates will be adding lots of side content that can be accessed from the daily agenda, such as hangout scenes and R&D projects, so if your only save is from the end of 0.5, you won't have free days to see that content until we put out chapter 19.