It seems silly to post about playing catch, but lately we've been having a ton of fun with it.
A few things I found:
1) When starting, a balloon (without a string) is easier to catch than a ball since it is squishier and moves slower.
2) It's easier to catch a bouncing ball than from the air.
3) Soft balls that can be caught with 2 hands are pretty great.
4) Frisbees are hard to catch, though we've had some fun trying with these:
5) And there's always this too: