In addition to what Trinitie said, when you do introduce your fish to the new tank, don't just release them from the bowl into the tank. Put them in a clear plastic bag with the water from the bowl/vase first and let them float in the new tank for at least 30 min. This will allow them to adjust to the new tanks temperature without shocking them. Just dumping them into the new tank from the bowl could result in shock which can kill your fish.
A new tank should also run for at least a week before any fish is introduced. I usually let them run on their own with no fish for a few weeks. This allows for all plants to be established as well as allowing good bacteria to be well established before the fish are introduced. This process can be rushed if you use water conditioners and additives available from aquarium suppliers.