Not a dumb idea at all in my experience. I think your estimated cost is pretty right, but you'll just be getting started if you want to make it pretty. Assuming you have a good flowing aquifer, regardless, don't run your pump 24/7. I know I can run mine as much as twelve hours in a "dry" period before I'd start getting hiccups in flow (the start of bad news for the pump and motor) where you are outrunning the well's recharge rate. You might look at a smaller pond like mine, about 120,000 gallons, one tenth acre. At that size it is actively manageable much like a large swimming pool. Won't cost you more than several hundred a year for bacteria enhancements, flocculant if needed, and pump power. If you really want no more than a swimming hole, no fish or plants, then go with a large sand filter, variable speed 3 Hp pump, 3 inch plumbing, and a chlorine generator that feeds on salt. The salt is only 1/1000 of sea water and feels good...tastes good off your wife's skin...LOL. I'd still go with aeration and the fountain. Pretty sure they make large pond size skimmers...which I expect you'd have two or more and you'd have to check regularly if you have leaves falling. My 25,000 gallon swimming pool required 16 of 40 pound bags of salt. It is indoors, so I don't worry about dilution due to rain overflow.
