Just to add some data here which may help explain things.
Studies have shown that plants take up ammonia/ammonium faster than the nitrifying bacteria and archaea. So if you "cycle" with no plants, and then later add plants that are relatively fast growing (floating as others mentioned being the best for this), they will out-compete the bacteria/archaea and the latter will enter a sort of hibernation. I've no idea how long they might live in this state, opinions vary and it seems to depend upon various factors. To me it makes no sense to go through this period of so-called "cycling" if you have live fast-growing plants in the tank. And the ammonia may harm them, as I have already pointed out.
Floating plants are ideal here, as
@Essjay noted. Substantial floaters like Water Sprite, Frogbit, and Water Lettuce, and some stem plants left to grow floating are good too. Aquatic plants take up ammonia/ammonium day and night, so they are continually removing this from the water. And it is next to impossible to have too much ammonia/ammonium from the fish and decomposition, assuming the tank is biologically balanced.
Any thing like bleach that is actually strong enough to kill snails or algae will inevitably harm the plants. Ask any botanist if you don't want to believe me. Snails (of the sort this is referencing, like bladder, pond, etc) are harmless, and they perform a useful function by eating all organics including fish excrement which breaks it down faster for the various substrate bacteria, thus providing it as food for plants or nitrifying bacteria/archaea, depending.