What about permaculture? Mixing field beans in with barley can yield 85% more than a barley monoculture. And small-scale farming can actually return more food per hectare. I am unsure as to whether permaculture and aero/hydroponics are compatible.
If the farming was done organically, any waste-water would be harmless to the environment and humans and could be either dumped or recycled.
I don’t think livestock farming would be either feasible or necessary — at least initially.
Water need not be imported — many ships have desalination plants, making the seawater drinkable. The simplest and most environmentally friendly would probably be something like a solar still.