Thrown or dropped chains are less a function of which brand chainrings you have, and almost entirely dependent upon your front derailleur's precise adjustment. A properly-adjusted front derailleur doubles as a mighty-fine chain catcher too.
Try turning the "L" screw on your rear derailleur in (tightening) a quarter turn and see if that fixes it. If that fixes it, but causes the chain to make a grinding noise against the front derailleur when you cross-chain, back it out (loosen) it 1/8th of a turn.
And if you're not sure which one is the "L" screw, the University of Youtube has multiple vids on "Adusting a Front Derailleur".
The best part about learning to fix & tune your bike is discovering a mechanical empathy and gaining a healthy aversion to cross-chaining in the first place.
You might make mistakes at first, but it's fun stuff to learn. Don't be afraid to experiment, to look around in Youtube and to ask in here.
Let us know how it works out.