Parrot's Feather is highly invasive and is illegal in some states because of the damage it has caused to local lakes/streams with folks just throwing it in there once it got crazy in their own ponds.
Hornwort is similar in nature, and invasive, but not as bad as parrot feather.
Cabomba is the same, also invasive.
If you're going to plant them and need to tame them back (which you totally will!). Throw them in the trash and not in any body of water.
Hardy Lily is a great choice since it's easy to keep in check. Iris does well. Rush is another good one, but can also be invasive (tho not as crazy as the three you mention above). However, there are some rush that if even a teensy piece falls on the dirt, it can send runners all over. I removed it from my pond two years ago as it formed a massive rootball.