Based on experience with running MPTA in Bratislava region:
Local authorities involved - the best is to have all of them to prevent that somebody have more power than other, best is to have equal votes or votes based on area serviced or votes based on other criteria (e.g. number of vehicle kilometers per year or number of passengers carried per year). Bratislava MPTA is owned by Bratislava region (65% share) and City of Bratislava (35% share). Ministry of transport is partner in Integrated transport system, but have no shares in MPTA.
Authorities can together create an association or a private law company or a public law company, each combination have it´s pros and cons. In Slovakia we are using model from Czech republic and Austria - where integrator is private law company with competences given by authorities through agreement.
Contracts between authorities is a solution, but in Slovakia´s case there is no enough will to cooperate from regions.
At last for each form:
Association is easiest way to create common platform, but there are more ways how to avoid fullfilment of agreed tasks
Private law is easier way how to set up common company, harder public control
Public law is harder to set up by different authorities, problematic way how to control the company, better public control