Chlorine is chlorine is chlorine. You mentioned using pool store stuff that bleached your liner. I assume it was Cal Hypo which is very slow dissolving. It needs to be predissolved and then you need to brush after to make sure it is dissolved and not sitting on the liner. If you are careful in it's use there are no problems. Liquid chlorine or bleach is ususally just dribbled around the pool or poured into the return stream and it mixes instantly since it is already a liquid. Bleach is even safer than liquid chlorine because bleach is either 5.25% OR 6% sodium hypochlorite while the liquid chlorine is usually 10% or 12.5%. Actually, a floater with trichlor can damage a liner but not from the chlorine. It has a pH around 2. If you use a floater be sure that it does not get stuck next to the liner.

If you decide to switch to using bleach with the trichlor NEVER pour the bleach in the skimmer. Trichlor doesn't play well with other forms of chlorine in concentrated forms. Once it is in the water it is fine.