Welcome to TFP!
As far as a test kit get either the Taylor 2006C or one from here:
TFtestkits.net. You're going to need to know how many gallons your pool will be, get it in the ballpark range as you don't need Tobe 100% accurate.
If you're planning on getting a salt water generator you'll need a salt testing kit as well.
Chlorine, use either liquid chlorine or household bleach if you can find it without any other additives in it.
You're going to need stabilizer, which you can get at Walmart, Home Depot or other sources that may carry it. Look to get as "pure" as you can get, usually in the 98 to 100% range.
I would start there. Download the pool math app to help you in what quantities you need for your pool. Add slightly less than stated and work up some more if needed.
Once you get your test kit, test the tap water so you know where you are with your chemicals. You don't need to test the tap for stabilizer but do test for pH, Alkalinity and Calcium.
For pH, you can use Borax, For Alkalinity you can use baking soda ... to raise both you can use washing soda but you need to know your tap water before adding anything. If you need to drop pH and Alkalinity use Muriatic acid but just wait on that for now.
Stay out of pool stores and don't add anything that's supposed to be "great". Pool care can be simple following simple rules and using basic guides. Take a look here for some information:
Pool Care Basics Archives
It's easy once you get a handle on it!