I have the 22' Intex Ultra Frame from
Walmart (only available at Walmart, 22' is not standard size and not listed on the Intex website even.)
The height is listed as the rail height, which is 52". The water level would be 48" on a 52" pool. It has to be 42 inches at least for the skimmer basket. My youngest at 8yo, the 48 inch water depth would be above her head. I filled it just enough to get to the skimmer basket, which is about 3 inches below her chin. It's rained since setting it up, so I've gained about an inch and a half. Still good for my youngest.
I was going to get the 18' x 52" at Sears, then found the 22' at Walmart right before buying for the same price. Glad we went with the 22'.
Sounds like you are interested in Intex since you mentioned the 12' x 36" (that's what we took down and gave to my brother-in-law.) No matter whether you go with Intex or a "real" above ground pool, make sure the ground is level all the way around. Dig stone pavers into the ground at each pole to keep them from sinking into the ground. That's a lot of water weight to be pushing down on them. 10,000 gallons of water weighs 83,000 pounds. The poles will sink into the ground with that much weight of water and the pool will collapse.
I have the Intex salt water system. Obviously with the low cost, they are not as customizable as buying from a higher quality company, but at a third of the cost, my SWG works fantastic. The water feels great, there is no chlorine smell, both my daughters comment on how soft their hair feels after getting out of the pool and their hair dries.
Still going with the Intex thought, the cartridge filters are not all they are cracked up to be from Intex. The sand filters on the other hand, the folks who are more expert than I am tend to agree that they are pretty darn good systems. My pool came with a cartridge filter which I'll use this year. Next year I plan to move the equipment away from the pool, upgrade the cartridge filter to the sand filter, and hard pipe everything (including building a DIY solar heating system for a fraction of the cost of a commercial system.)
If you have a larger pool such as this (the 12 foot it was nothing to drain and refill) I highly recommend joining up at
www.troublefreepool.com. Take control over maintaining your water instead of visiting a pool company. A pool company wants to sell chemicals and I've read comments on how they have told customers to add X amount of this chemical which would overshoot a measurement by a large amount just so they could say now buy and add Y amount of that chemical which is to pull the same measurement the opposite direction.
At
www.troublefreepool.com you will learn how to test your water and determine exactly what you need to keep the water crystal clear. It cost me $68 for a text kit and about $10 worth of stabilizer and bleach and baking soda to get my pool up and running before I could get the salt water system going. At the pool store, that would probably have been hundreds of $$$ to achieve the same thing.
I could never get my little 12' pool water clear, it was always cloudy and couldn't determine the chlorine level (the test stuff they sell at Walmart is highly inaccurate as is a pool store water test.) I got it all figured out from reading at the Trouble Free Pool website.
The pool store chemicals are the exact same thing as you get in the grocery section of Walmart, except that the pool store cost is about 4 times more. You learn this at the above website/forum. It's been a treasure trove of information on maintaining the water in the pool for me.