some points
so let start by say zimbra is not just mail server its "Collaboration server" (email/calender/plugin/) and more
you can ask digitalocean to add disk (just turn off the server and go to resize in the digitalocean menu)
and you can do alot using zimbra you can set qutra per mail box so user will need to clean up the email and you can archive users email using scrips (i get some )
if you just like to give email service you can look at RainLoop(nice the new kid on the block),SquirrelMail(old but still good),cypht(new but nice )
but that say in the past i manage alot of zimbra server and for big user gruop it was one of the best i ever use if you still need help on the zimbra you can contact me off line and i will be happy to help