"semi-symetrical" is actually a mis-nomer. Either you are symetrical (ie, 0 camber) or you have some camber. Some airfoils have a lot, some don't have much. As Minn said, most trainers use a fairly high lift airfoil with quite a bit of camber. They also tend to be set up such that increasing airspeed results in a change in pitch trim, ie ballooning, which also means it will try to automatically pull out of a dive.

Stability is more a function of dihedral as Minn said (for roll stability), and the relationships between the wing and the tail (incidences and areas mostly) (for pitch and yaw stability).

There are some very acrobatic and maneuverable planes out there with cambered airfoils, though most acrobatic planes have symetrical airfoils to make inverted flight easier, and allow them to do maneuvers inverted almost as well as upright. And you can make a very stable airplane with a symetrical airfoil as well. So the airfoil is only a small part of the story.

That said, I looked up the Happy Fly, since I'd never seen one. I think Minn's recommendation is right on. You should be fine with any of the low wing sport planes like the 4* series, the super sportster, or the others mentioned in the many threads on "second" or "third" planes on the forums.