Correct sequence of steps for a multi-step workflow

I'm working on a project where a logged-in user(nurse) has to complete a multistep workflow in order to enroll patients into their doctor's records system.

The workflow needs to capture: Patient Name/Contact Info, Doctor/clinic information (neither can be assumed), Prescription information, and some test results/general medical questions.

Important info: This process is meant to replace a paper form that currently exists - so some users may be used to filling in this information with pen and paper.

I've heard the thinking that it's important to engage users, which would lead me to choose the medical information or the Prescription information as the first steps rather than the data entry that is patient contact info and doctor information but I'm hoping there are opinions or thinking to support or refute that approach.