Hi,
There are only a couple varieties that are grown from seed and in turn I would assume make seed. The others are all propagated through cuttings and do not make viable seed. The $4-5 plants you like I'm going to assume are varieties from cuttings.
You can over winter the plant or cuttings if you are into doing that. Otherwise, you'll need to buy plants every year. To take the sting out of that you could tell people you would love gift certificates to your favorite garden center instead of other gifts.
Remy

At the risk of veering a bit of topic: how easy are bacopa to propagate from cuttings? Do they root quickly, in water?

Yes, they should be easy to root.
Remy

Anyone know the name of this plant ?

Cornflower. It is a weed/wildflower here in the Midwest. It is also known as Chicory to some.

cichorium intybus aka chicory