Bleach has the least "side effects" of any chlorine source.

Pure, unadulterated trichlor (usually in tablets) is fine if the pool needs CYA - it should be avoided if the CYA is OK or high. What's in the tabs you have? If they contain copper, I wouldn't use them.

I can't emphasize enough how important it is to buy and learn to use a Taylor K-2006 test kit - you'll need it to take control of the pool. If you buy it through the links in this thread the Poolforum get a few shekels to keep the lights on.

The salt in the pool won't make a bit of difference to how you chlorinate (some people like the feel of salt water).