Keep in mind — especially for fish caught on light line — they just got through fighting for their lives and are spent. Much like you or I after a workout, they need more oxygen. Getting them back into the water or into the livewell fast will increase their recovery chances.
If you add tags to your fish before you put them in the livewell there are some simple tricks to doing this in the best possible way. First, I sharpen all of my culling tag pins, this makes them go into the fish fast and easy and with as little of a tear as possible. Next put it as close to the tip of the fishes jaw as possible. The further back on the fish you insert the pin the bigger the hole. This affects the "vacuum" suction that a fish uses to inhale its food. I have caught a lot of fish with big holes, big enough for my finger to fit through, and it bums me out when I see that.
For livewell care, I don't recommend adding anything other than possibly ice and rock salt (which is non-iodized). However, there are some things you can do to make your livewell function better. First, be sure that your livewell has both the fresh and recirculating water entering from the top of your livewell. You want the surface water of the livewell to be as disturbed as possible because it increases the oxygen level for the fish. I re-plumbed mine a while back and since then my fish have been healthier than ever. This alone will increase the health of your fish.