I advise replacing the system entirely at one time. The controls required to make the copper loop and the castiron section operate confortably at the same time add some expense and the possibility that this mix will remain for a long time is a terrible thought.
It is possible to install cast iron radiation on the copper loop and this would make the piecemeal transition easier. the cast iron baseboard will make a very comfortable home due to its long cycle of giving off heat.
But again it is better to do a complete, well-thought out design at one time. Concepts an installer needs to know are at http://www.hydronic.net
I am curious about your decision to change from the radiators to baseboard. European preferences are for wall radiators or floor radiant heat. Replacing the pipes in a working system is possible; they worked for 50 years. Is it an aesthetic choice? – No standing radiators, modernization, etc?