Phew! Those are quite a few questions.
In my opinion, STS is a perfect buy for you if you want to get serious about weight training. I am aware of people who were in good shape (from doing some kind of light resistance training and fairly advanced cardio on a regular basis) who started training with weights with a periodized program and did great. Since you will be lifting based on your one rep max, this program is tailored to your current strength and will help you develop muscle endurance, build muscle and strength. What one rep max means is, if someone who is very strong from years of lifting can squat a single rep with 120 pounds and bench press 80 pounds, and if you can squat a single rep with a maximum of 40 pounds and bench press 20 pounds, you can both do STS. STS has three phases. From one phase to the next you do less reps per set, but increase the weight you use on each exercise. So when you start you will be lifting relatively less but doing more reps. Based on your individual 1 rep max, this website will guide you to pick the right weight for each phase.
Equipment:
Equipment that is mandatory: you need weighted dumbbells, a dynaband and a step-bench.
Platemates (or pace weights) that allow you to increase the weight of a dumbbell in small increments (like 1#) by magnetically attaching to the dumbbell are a good buy but not necessary. It would help to buy dumbbells that are compatible with platemates so you have the option to get them later (they must have metal outer sides to which the platemates can attach like magnets).
A barbell and barbell plates is preferable but not necessary.
For the ab work, a stability ball and mat are needed.
The rest is all optional.
You can use basic equipment for your first time through STS and buy more for your second time through.
You can purchase a basic set of dumbbells (5#, 8#, 10#, 15#, 20# is a good starter set in my opinion) and buy more as you go.
Preparation for STS:
You may want to buy one or two full body weight training DVDs from Cathe (like Muscle Max, Supersets/Push-Pull) now and work with it until STS is ready so that you are better prepared.
To learn about STS:
1. Visit Cathe's home page and click the STS links - those provide a great overview
2. Go to the first few queries on the STS forum and start reading if you can make the time or do a search on the STS forum for specific questions that come to mind once you read the overview on the home page. For instance "equipment" as an advanced search option of the STS Forum will throw up many doubts people have raised about how effective the program will be if they stick with basic equipment and SNM's answers to those questions.
3. Spend some time looking at the pictures of STS exercises in the blog. Keep in mind that there will be modifiers shown for all exercises that use the non-mandatory equipment like squat racks or pull-up machines. There will be no modifiers showing dumbbell modifiers for exercises that use only dumbbells, but for a very long time when I first started weight training with Cathe I used only dumbbells and got great results. My barbell was a recent acquisition. It is easy to modify all barbell exercises on your own using dumbbells.
4. If you cant find an answer to a specific question, or dont have time to look and feel overwhelmed, just ask here again.