I'm in marketing and do most of my work in a proprietary CMS.
1. See if it has to integrate with any software. Find out what marketing really really needs to still have, and what they could switch out if necessary.
2. See what they do. What kind of changes they need to make and how often. Find out what sorts of changes cannot wait weeks for an IT ticket.
This could narrow it down, and then you can get input from the other departments and iterate toward a decision.
Then have them play with it. They'll probably say oh shit, why can't I just do _____.