Ski poles have a way of affecting balance. Therefore, their length is important.
In the old days, alpine skiers used to ski with very long poles. Then poles became very short; now they're a tad longer than ''short.'' My own poles are slightly on the short side; but if you have to err, that's the right direction, in my opinion. Poles that are too long are apt to push your weight backward (which is where mine is too much of the time without any help from poles, thank you). Too short, however, can pull your balance point too far off center.
A good rule of thumb is to rest the grips on the floor and grip the poles just below the baskets. If your elbows form a right angle (90 degrees), that's the right length.
Cross-country ski poles have some functions different from their alpine counterparts and must be longer. They are part of your motor power. A general rule for proper length is that a standing pole should fit comfortably under your armpit.
And yes, there is a right and left cross-country pole. The top strap goes across the back of the hand, the bottom strap under the thumb. You should be able to let go of the pole and still have it within easy grasp. The curved point of the pole faces forward to minimize drag.
Ski poles these days come in some very fancy materials and prices. For most skiers, however, a moderately priced pole will do fine.