IMHO, The TF-100 is a bit of $$$ but you will also be saving money in not having to drive to the pool store to get your water tested. At almost four bucks a gallon the test kit doesn't look so expensive and can pay for itself while keeping your pool clear and blue.
You don't need to order CYA / stabilizer from amazon unless you just can get to Walmart or HomeDepot or .... They should carry it on the shelf.
http://www.homedepot.com/p/HTH-4-lb-Stabilizer-and-Conditioner-61316/100239944 This is just the HTH product but there are others too.
If you need baking soda for raising pH Walmart among others will have that on hand too so no need to stock up. It would be in a 12lb bag with the pool stuff.
http://www.walmart.com/ip/Arm-Hammer-Baking-Soda-192-oz/17043412
I would just rake without the pump on. Less circulation and whatever you miss with the rake and stir up will settle back sooner. Rake until you don't get anything and remember anything you pull out makes the SLAM faster, easier and cheaper as you won't need as much bleach. Once you aren't getting anything in the rake and that might take a day or two or three depending on when your arms or patience give out then I'd vacuum and brush and run the pump to try and catch whatever you loosen. Once the big stuff is out with the rake try to brush at least once daily and pull your ladder if you have one and scrub it good especially checking under each step and if you have a light pull it and clean the niche.
It's just so much easier to vacuum once you've pulled out the big stuff and don't have to empty the skimmer basket every minute or two.
