Hello.
I'm still on the process of getting a Mini...
My take on it would be, what are exactly her needs?
Just backing things up? I guess you say that's not the case.
Then my bet would be you wanna set it up as a streaming device, for sharing files on other computers (not only the Air) or maybe share an iTunes library and stream it via an AppleTV.. or something like that.
In any of those cases, I think the base mini should be sufficient, probably the server would be overkill.
But since you already have the server... and you say you don't fancy anything on the cloud (probably in the same vein of accessing the server outside your home to stream music to your mobile phone for instance), then my inexperienced take on it would be, that pairing it with an AppleTV (there are other options, but with that price, I would go for the ATV, the Apple route after all) would really take that sweet juice out of that server for AirPlay mirroring on a big screen and streaming of multimedia content (that is not to say of course, you just use a HDMI cable and ditch the ATV).