I've had a 12 gallon AP for 4+ months now.
I kept mine pretty stock so I will list some stuff I've purchased, and mods I recommend. Some stuff will be obvious so just bear with me
For starters, you'll need:
Sand
Live Rock
Water - I mix my own salt water with walmart RO water.
Heater
Digital Thermometer
Refractometer/Hydrometer - Go for the Refractometer if you can afford it.
Another thing you should look into is a magnet cleaner, the nimblenano is nice.
http://nimblenano.com/
The Maxi-Jet 900 must is definitely a must. It is said to run cooler and keep water temp down.
Next, ditch your sponge, and ceramic rings. Get yourself some filter floss, and then try to get enough live rock rubble to fill one of your chambers.
Another mod you will want to plan to do is block the bottom vents on the chamber #1. This will force water to pour over the top of the chamber and act as a surface skimmer. I actually blocked up my lower and middle vents leaving the water to pour over the top.
You should also think about when you are bringing stuff into the tank. You should be dipping most of the stuff to kill of pests so I would recommend:
Flatworm Exit by Salifert
Lugol's Iodine
What else what else....
A net incase you need to catch a fish or something. I would recommend you get one that is a fine mesh. I sometimes use it to filter stuff.
A few Buckets for water changing and water storage. Some small tupperware containers for you to dip new stuff coming into the tank.
A turkey baster is always handy. Some gloves to protect yourself.
A small towel to keep handy since your hands will most likely be wet every time you are poking around at the tank.
A long pair of tweezers if you can find them to reach in the tank.
And lastly, some good test kits to make sure your water is doing ok.
Hope that helps with a bunch of odd ends
