Short answer
The terms that matter most are deliverable-based payments with acceptance criteria, caps on renewal increases, named key personnel, clear data ownership and exit rights, and service levels with real remedies. Agencies that win negotiate these before selection is announced, while they still have leverage.
Your leverage is highest before you tell a vendor they have won, so I like to send draft contract terms with the RFP and ask vendors to note their exceptions in their proposals, which turns the contract into part of the evaluation rather than an afterthought. On the implementation side, the key terms are a statement of work written as deliverables with acceptance criteria, payments tied to accepted deliverables with a meaningful holdback until stabilization, named key personnel who cannot be swapped without your approval, and a change order process with agreed rates.
On the software side, I focus on price protection, so caps on annual increases, locked pricing for modules and users you may add, and clarity on what happens at renewal, along with service levels for uptime and support that come with credits you can actually collect. Data deserves its own section, covering ownership, export in usable formats, transition assistance, security and breach notice, and for AI features, a commitment that your data will not be used for training and that you will be told when the underlying model changes.
It is worth having your attorney and someone who negotiates these deals regularly read the vendor paper together, because the risk is usually in the order of precedence and the documents incorporated by reference rather than in the main agreement. The Start at Zero Navigator includes a contract checklist, and it is free.