There are 2 trumpet vines, Campsis grandiflora which is Chinese trumpet vine, an invasive exotic. Then there is Campsis radicans, a native. If you go with trumpet vine, make sure you are getting the native one.

Bougainvillea has spikes. If you have little ones, that might make it impractical if you think anybody will get poked.

Morning glories come in many types that can be extremely weedy regarding the seeds. Some varieties, like 'heavenly blue' are sterile and will not cause this problem.

Regarding poisonous plants, this discussion may help.

Heavenly Blue is a variety of Ipmoea tricolor, and is not sterile. This weird bit of misinformation has popped up several times recently on this forum. Anybody who grows Heavenly Blue can tell you it's usually generous when it comes to seed production.

Perhaps it's being confused with Ipomoea indica, which in its most common form produces a profusion of large blue flowers. This one rarely produces seeds; it doesn't like it's own pollen and requires pollen from a nearby unrelated clone of I. indica in order to set seed. It's an enthusiastic grower which requires occasional maintenance to keep in bounds.

I've never had a volunteer heavenly blue after planting store-bought seeds.

Doesn't come back from volunteer seedlings given the conditions in your garden isn't the same thing as sterile. Schefflera doesn't come back from volunteer seedlings in zone 8, but anybody who's lived in the tropics can tell you it isn't sterile.