What water parameters to test for?

[NittanyLion]

I currently use the four way test strips for ph, free chlorine, alkalinity, and cyanuric acid and see no water problems.  When I read this site and look at other test kits though there are many more parameters, including the following which I do not test for:
           total hardness
           total chlorine
           total dissolved solids (TDS)
           copper
           acid/ base demand

My questions are the following:
           Are any of these parameters things I should be testing if my water seems OK?
           Is having high cyanuric acid bad for me, my tub, or my ducky?
           Does total chlorine just to tell you when to shock?
           Does TDS just tell you when to change the water?

[wmccall]

Hardness is something that is good to know and if your like me, you can forget about it.  It generally doesn't change much.  My water is consistent out of the tap and i add a minimal amount of calcuim to get it to the minimal acceptable level.

CYA starts low and just keeps getting higher till you change the water.  I don't worry about it, when its real high is about the time I'm changing water anyway. The same goes for TDS.

PH and Alk are about all I check any more as I have my dichlor/MPS routine down pat.