
I don't think anyone's mentioned tyres yet: I completely agree that you should keep the bike as original as possible to preserve its history and character, but it's very important to to have nice sticky tyres to exploit the Morini's wonderful handling, and if the bike's been laid up for a number of years, your existing ones probably won't be up to the job. (And if your dad used to race the bike, they won't be original fitment anyway).
Best of luck with it.
Mark