Short answer
Look for a platform that fits how your institution wants to serve students and manage money, with strong integration between the student system, finance, HR and financial aid. The keys to success are getting cabinet agreement on priorities, cleaning data early and deciding which local practices are worth keeping before the vendor's timeline starts.
Colleges and universities have a harder version of the ERP problem, because the student information system touches admissions, registration, financial aid, billing and advising, and it has to talk cleanly with finance and HR, so I would look at how well each option handles those connections as much as at any single module. Ellucian, Workday, Oracle and others all have serious offerings here, and many campuses on older on-premises systems are now being nudged toward SaaS, which is a good moment to rethink processes rather than move the same workarounds into the cloud.
I would start with the cabinet, since provost, CFO, CIO and student affairs often have different ideas of what the project is for, and getting agreement on a short list of priorities, like a better student experience at registration or faster financial reporting, will make every later decision easier. Data is the next key, especially for student records that go back decades and the shadow systems that grew up in individual departments, and I would name owners and start cleaning well before implementation.
Finally, insist on scripted demos built on your own academic calendar and aid scenarios, and plan go-lives around terms and aid cycles so students never feel the cutover. Our Banner Phase Zero checklist and the Start at Zero Navigator both cover this ground, and they are free.