I was thinking of using the 5V zener to protect my ADCs from unwanted high voltages.
Don't do that, use two schottky diodes to clamp to Gnd and AVcc (assuming
the diodes you pick don't have too much reverse leakage to affect what you
are trying to measure). Zeners don't have a very sharp knee in their breakdown
region, so they really aren't good for this.
You could also use normal small signal diodes to clamp, but make sure their
forward voltage drop is such that out of range voltages don't exceed the
absolute maximum ratings of the ATMEGA328.
Don't connect Vcc and AVcc directly, at the very least you should put it
through a ferrite bead or something to try to keep the digital noise out
of the analog supply. Personally, I would use a second voltage regulator
dedicated to the AVcc pin.
I tend to think of the builtin ADC on most micros as courtesy parts, i.e.
it's there in case you can make use of it, but don't expect too much,
like decent linearity, out of it.
If you want really decent performance, you could use an external ADC with
either an SPI or I2C interface. Up to 24 bit resolution is easily available,
although getting a useful 23 or 24 bits is an art form!
Scott