What variables should a Zendo game contain if it's being played with new players?
The most basic, and easily visible, attributes are best for beginning players are the most obvious and easy to see. Color, size, basic orientation, number of pieces.

Rules that involve simple combinations of these attributes are good (a koan has the Buddha nature if it has a small red piece). Rules that have too many relations going on (touching, pointing) at once are somewhat more difficult (a koan has the Buddha nature if it has a small red piece touching a large green piece). Rules that involve pip count arithmetic can be quite difficult for beginning players. Rules with an "and" in them (a koan has the Buddha nature if it has a red piece and a flat piece) are OK for beginning players, as long as they aren't too complicated; an "or" (a koan has the Buddha nature if it has a red piece or a flat piece) are more difficult and should probably be avoided at first.

There are a few features that can be fairly non-obvious or hard to express for beginners (groundedness, weird orientation) and so should probably be avoided at first and introduced slowly. Also, introducing non-standard relationships (corner pointing, nesting without touching) should be avoided until people have a little more familiarity with the game.

Another way to simplify the game for beginners is to remove one color. With only three colors, it becomes much easier to figure out and test rules that involve colors.

One thing to remember with Zendo is that it's almost always better to err on the side of a rule that's too easy rather than a rule that's too hard. It's frustrating when no one figures out the rule in Zendo. It's very easy to come up with a rule that's too hard, especially if you're trying to be "clever" about it (one of the more frustrating rules I've played with was "the sum of yellow and blue pips must be a fibonacci number"; that was especially bad, because 0, 1, 2, 3, and 5 are all fibonacci numbers, and you run out of pieces quickly when trying to test higher numbers to figure out the pattern).