Unfortunately there isn't any 'under' the seat. The whole thing is a pop-out on the side of the house. It's sturdy, but it is actually hanging out over nothing.
So with the comments I have gotten from here, I have also purchased:
item # item description qty
------ ----------------------------------------------- ---
601141 No Spill Clean and Fill 25 ft. Kit 25 ft 1
605183 CLASSIC EXTERNAL CNSTR FLTR 2217/UT 159G 2217/U 2
601139 Visi-Therm Deluxe Heater 300 Watt 300 watt 2
603528 Freshwater/Saltwater Carbonate Hardness Test Ki 1
603529 Freshwater/Saltwater Nitrate Test Kit 1
603530 Freshwater/Saltwater Ammonia Test Kit 1
605784 ESU Power Center(TM) 1
604736 AmQuel Plus, 16oz 16 oz 1
604668 Prime, 250ml, 8.5 fl oz 250ml, 8.5 fl oz 1
I've already got a PH test and will buy the nitrite test locally.
I also got 200 lbs of play sand (Silica) from Home Depot.
For the nook I got a 8 foot length of pool liner (.45mm thick) to protect the wood in case I accidentally leak water. The stairs will just have to buck up. I'm going to get a 20" by 82" piece of plywood to set on top of the liner to make a nice flat base for the aquarium itself, and I can then attach a flashing board to the front to make it look nice.
The filters I chose because they will fit within my 10" of space beside the tank. The 25' python hose will be plenty to reach the nearest faucet.
What other things do I need to buy before I can start putting some plants in it and cycling this thing?
Some ammonia, in some form or another. (Can't I just put a few drops of urine in the tank?)
Some aquarium salt.
Do I need to get an air pump for oxygenation? I'll have several plants before I add any fish, but these filters I don't think put any oxygen in the water at all.
Anything else?