The biggest problem with a cub is the ground handling. They can be difficult to take off and land, but in the air it should be fine. (assuming you have the control rates and CG set well)

A .20 powered cub could be fine in a park (depending on the park, of course), or not a good idea in a park, depending on how big the plane is. Cubs can be flown on an amazingly wide engine range. What's the wingspan and weight on the cub you are talking about? Be sure to prop with a low pitch, high diameter prop as well to keep things moving slowly. It is quite possible to make some glow powered planes fly like noisy electric park fliers.

Do be carful with a glow engine in an uncontrolled area like a park though. Be prepared to chop the engine and dump the plane if things start going wrong. And take a spotter with you to tell you if something or someone is wandering around under your plane, espeically on the landing approach.

You say you can fly helis, what exactly can you do with your heli? Can you nose-in hover? how about full forward flight? backwards flight? In general, flying a chopper will make you a better airplane pilot, but if all you can do with your heli is a nose-out hover, you've still got some learning to do, and I suggest you find an instructor for a few flights with the cub.