Hi Max,
You can request a free-trial edition of Zimbra - including support.
There are two version of the NE edition (standard and Pro).
Comparison of the two
here.
You can also get a free price quote
here.
There is a much better backup feature in the NE edition and you also have the forum here. I think you get 3 free support incidents per year - but can purchase more.
Push email is supported and I have been informed that v5 mobile package will be supporting Blackberry by default (as opposed to a third party option).
HTH
Costa