I want to apply for a Schengen visa, but according to the plans I am supposed to start my trip with Romania. Is it allowed or is it necessary to land in a Schengen territory first?
You can enter Romania with a double entry or multiple entry Schengen visa valid for Schengen states. It is not necessary to have visited a Schengen member state before visiting Romania on this visa.
So that you can receive the correct visa type and sufficient duration, you should still include your travel plans including Romania as part of your Schengen visa application, so that the consulate can include your proposed time in Romania as valid dates for the visa.