Hi gofast, and welcome to the forum.
The stabilizer is cyanuric, or isocyanuric acid. It is sold at pool stores, Home Depot, Lowe's, WalMart, and most any other place that sells pool stuff. It's often labeled conditioner or balancer--just look at the ingredient label for 100% cyanuric acid. You'll need to check the manual for the SWCG you get--they all require different amounts of stabilizer, most average around 80 ppm or so.
One absolute MUST, and one that's going to save you tons of money even just your first season, is a good test kit. We recommend the K-2006 that you can find in the "testkits" link in my sig. There's also a recommendation for salt strips there, as well. If you can get your kit, run a set of tests on your fill water(don't test it for CYA, there won't be any--save the reagent) we can tell you what else you're going to need for your pool.
What is the source of your fill water?
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