Upto my understanding; u should go with the Pvt. Ltd. Company that is broad in scope and permanent in nature. You can not go with the Project Office because:-
Foreign Companies planning to execute specific projects in India can set up temporary project/site offices in India.
RBI has now granted general permission to foreign entities to establish Project Offices subject to specified conditions.
Such offices cannot undertake or carry on any activity other than the activity relating and incidental to execution of the project.
You can go with Branch Office but the scope of work is restrictive in nature and sometime yoiu may face some restriction because :-
Activities permitted:
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Export/Import of goods
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Rendering professional or consultancy services
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Carrying out research work, in which the parent company is engaged.
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Promoting technical or financial collaborations between Indian companies and parent or overseas group company.
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Representing the parent company in India and acting as buying/selling agents in India.
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Rendering services in Information Technology and development of software in India.
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Rendering technical support to the products supplied by the parent/ group companies.
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Foreign airline/shipping company.
A branch office is not allowed to carry out manufacturing activities on its own but is permitted to subcontract these to an Indian manufacturer.
It may remit outside India profit of the branch, net of applicable Indian taxes
Being Private limited company you can perform all the activities in India freely. As far as the taxation point of view is concerned all are treated as Permanent establishment and taxed.
Others views solicited.
Regards,