Yep, definitely bleach. If you want to go long term disinfection (standard store bleach lasts +/- a year), I would recommend calcium hypochlorite (pool shock). There are many online resources that explain usage and safety concerns. To paraphrase it all:
1) A one pound bag could treat over 10,000 gallons and costs around $4.00.
2) Correctly stored, it will last forever.
3) The calcium hypochlorite percentage should be 70% or more and contain no perfumes, algaecides, etc.
4) The calcium hypochlorite is used to make bleach which is then used to disinfect drinking water.
My opinion is that it is one of the best "bang for your buck" preps. We have it, we've used it, and we recommend it to others. Definitely do some research on it and determine if it is the right choice for you.