My main issue is that if you target this with Giant Growth and it's the only creature on the battlefield, it becomes infinitely big and/or the game self-terminates. What would be the best wording such that that doesn't happen?

You could specify that Ricochet represents both the triggered ability and "This permanent can't be the target of copies of spells created this way" (which would automatically exclude it from the random choice, so no fear of landing back on itself and fizzling), but then the same problem arises by engineering a board with just 2 ricochet creatures.

Would limiting spells to a single level of ricochet (i.e. "Whenever a player casts a spell that targets CARDNAME...") make the ability too mundane?

Also, what about spells with multiple targets (like Symbiosis)? Do you reselect all the targets at random, or just the target responsible for the ricochet trigger? What if it's something like Seeds of Strength targeting this three times?

Does that deal with the issues?

Two copies of this on the table, grow one of them; bounces back and forth infinitely still, I think.

"And that copy cannot be copied" is inelegant, but possibly workable?

I don't think that will happen. The reminder text says "The copies can't target this permanent." That applies to copies of copies as well (I think).

In the context of a triggered ability, "this permanent" refers only to the object that created the particular instance of the trigger. The problem of an endless Pong game still arises.

What if it gains shroud as well? No, that would counter the original spell. For now I'll use SM's earlier idea and make it more mundane. No more board-sweeps, though.