Trouble Free Pool Care is a methodology (a process) and not a specific list of products! You can surely use any product really. You just need to understand what each product does to your pool water, and avoid putting your pool chemistry in a bad place by choosing the wrong products at the wrong times.
Cal-Hypo powder is a really good product in terms of how cheaply you can add chlorine to your water, and as you've noted it's a lot easier to store! One 50 pound bucket of Cal-Hypo only takes up about the same space as 3-4 gallons of bleach. The downside to the Cal-Hypo is that it adds a significant amount of calcium hardness into the water as you chlorinate the pool with it. For a vinyl liner pool... it's not "so much" of an issue... but you really want to keep levels at or below 400ppm. Feel free to use the Cal-Hypo as long as you are below that level though.
The main upside to bleach, is that it will not increase the levels in your pool outside of the free chlorine levels.
I used Cal-Hypo for a while, as mentioned make sure it doesn't sit on your liner... it will bleach it whitish yellow. Pre mix it in a 5 gallon bucket of pool water. Remember to add the powder to the water in the bucket and NEVER add water to a bucket with powder already in it.