Clorox is just fine. Great Value brand from WalMart is fine. Any type of bleach is fine as long as it's regular, unscented bleach. Do not use splashless or outdoor bleach. The only thing that's important is the hypochlorite percentage listed on the bottle and that the bleach hasn't been on the shelf for a long time. Bleach % hypochlorite will decrease over time so the fresher the bleach, the better. Most bottles will have a date code on the side and you can usually decipher what date the product was manufactured. For instance, on my 12.5% liquid pool shock, there is a number in the printed date code that is "15113" This means that the bleach was produced in 2015 on the 113th day of the year, April 23rd.
The shock packs may increase CYA levels or they may increase CH levels. Read the label for active ingredients. If the active ingredient contains "dichlor" it will increase your CYA. If the active ingredient is "calcium hypochlorite" it will increase your CH. There are other types of shock such as lithium hypochlorite or non-chlorine shock, monopersulfate. Those two will not increase CYA but are more expensive and therefore, not recommended for regular use.