I have been consulting this site since we reopened an old gunite pool that came with our house earlier this summer. At the beginning of the summer I was equipped with tablets and cal hypo, so I used that pretty successfully but stopped when my stabilizer reached about 50 ppm. Since then I have been using household bleach, and based upon the results I get with my Taylor K-2005 kit, I think things have been going pretty well.
Just today, I was warned by the local contractor (the one who replaced our pool piping and pool deck) about using bleach in a pool. He is supposedly basing this on experience where he has seen bleach weaken grout and the gunite, as well as vinyl liners (which doesn't apply to me). I argued politely with him a bit on the basis that when it comes down to it, free chlorine is free chlorine, but I just wanted to see if anyone else has received warnings about using bleach.
BTW, I am new to this forum, but it has been a lot of help this summer! I'm sure I'll be back with more questions soon!