A Contract is Anything to Which Two or More Parties Can Legally Agree
There's no singular answer to this question, and most of the question is out of scope for project management. It's more properly a business or legal question, and you should consult your company's lawyer about what's essential. However, there are certainly aspects to a contract that may impact the success or failure of a project, and you should certainly provide input about those elements to the contracting officer in an appropriate way.
What Parts of a Contract May Impact Project Planning
From a pragmatic project management standpoint, in the US you don't need anything project-specific for contracts in general. Master services agreements or partnership agreements are good examples of contracts where there's no need for specificity around specific deliverables.
For project work, you still need to consult your legal counsel, but in general you need things like:
- A "Statement of Work" (SOW), which usually describes the deliverables, payment terms, and other factors related to a given set of deliverables.
- Detailed payment topics such as time-and-materials, flat fee, or time- or milestone-based payments; triggers or deadlines for payments; methods of payment; and other more granular payment topics that are generally the domain of your finance and legal experts rather than the project manager, although the project management framework may certainly play a part in determining how these matters ought to be addressed.
- Some form of a "Definition of Done" (DoD). In other words, how will the success or failure of the project or the quality or suitability of specific deliverables be determined?
- A contractual agreement about how changes to scope, schedule, or budget will be handled.
- Assumptions, caveats, and known risks for the project that might trigger changes to the SOW or the cost and payment structures.
- How disagreements or termination of the contract will be handled.
- How project risk will be divided between the companies.
- Whatever else your legal advisors and senior executives think is necessary to protect your company's interests, and the company's successful execution of (or at least avoidance of non-payment for) the company's responsibilities as defined by the contract's terms.
None of these are strictly required, but they are certainly extremely common. It would be awfully difficult to commit to a contractual agreement to deliver a product or service without knowing what is expected, how much it will cost the buyer or the seller, or how other project-related matters will be handled.
Project Managers Aren't Usually Lawyers or Company Officers
The project manager certainly has a role to play in helping the company determine whether the proposed budget, schedule, and possibly the deliverables defined in a contract can be done with the resources that will be made available to the project, but the project manager generally lacks the training, expertise, or responsibility for contracting per se. I'd highly recommend not getting involved in the contracting process outside the scope of the project management discipline. Project managers are quite often held responsible for the success of a project without being fully empowered to exert meaningful delegated authority, so keep that firmly in mind.
Sticking your nose into the legal domain, or into a role generally reserved for company officers, will just make that organizationally unsupported accountability worse. In short, don't do that. Address yourself to the feasibility of successful project delivery based on the statement of work and other relevant items, but leave the contracting to the contract professionals.