Calcium is irrelevant for a vinyl pool (unless it gets too high which can perpetuate scaling).
Bleach is almost always the least expensive method of adding chlorine. Usually walmart or aldi are the cheapest sources of bleach, but sales elsewhere can be good too. Easy to compare prices... $/oz./%. So if wm bleach is $3.25 and home depot is $2.99 (and assuming walmart is 1 gal whereas home depot is only 121 oz), 3.25/128/0.0825 = 30.78 cents per ounce of sodium hypochlorite and 2.99/121/0.0825 = 29.95 cents per ounce of sodium hypochlorite. Home depot wins in this case AS LONG AS what home depot is selling is regular household bleach (no additives, scents, detergents, etc.).
Or another way to look at it... 1 gal of 8.25% bleach provides about 2 ppm fc for yor pool at $2.99. That's about $1.50 per ppm fc. 16 oz of 53% cal hypo provides about 1.6 ppm fc for your pool... So unless you are getting cal hypo less than $1.50 per 1# bag, it's more expensive. At $3 per lb, you are paying nearly 2x as much as the same fc in bleach. You have to decide how much more you are willing to pay for the convenience of 1 lb packages vs. 1 gallon jugs.
Unblended dichlor is 99% dichlor... No other additives or components. Usually only available at SAMs club or online. Nothing but pure dichlor is ever recommended here that I have seen. If your cya is in the 50-60 range you might not want to add more. There are reasons to run higher cya levels but usually 50-60 is where you want to hold... And right now you need to eliminate the algae rather than worry about increasing cya.