.. Are there special box type units that vent in the back ?
She was told those are older style units and that central A/C or window
style is more common.
The water generated from condensation is also an issue.

Yes,there are A/C units specifically for through-the wall installation.
Normally if you have the sleeve in the wall already, just get the name
of the sleeve or the original A/C that was in it ( usually Friedrich
and Fedders are common) and the local appliance stores should have
them. The wall A/C's vent through the back. If you try to operate a
window A/C in a sleeve, it will not run correctly.
The newer A/C's made today are designed to hold the condensate in the
pan to allow the coil to cool more efficiently, so the condensation
should be no problem.