I first read a few of Sophocles' plays when I was in high school. I enjoyed them. I wasn't a fan of plays at the time, and Sophocles opened me up a little to the world of drama.
Personally, I don't think Shakespeare can hold a candle to Sophocles. Sophocles makes Shakespeare look like an illiterate hillbilly, which, considering the fact that Shakespeare straight up made up over 2,000 words, it's kind of true.
We know for sure that Sophocles wrote nearly 100 plays (over 80 of which won awards), sadly only seven of them have survived into modern times. The ones that did survive, survived because of their superior quality. They are the best of the best of the best. They were the ones which were most often studied by ancient scholars.
Sophocles' life coincided almost exactly with the golden age of Athens, and his plays reflect the rich, deep history of not only Athens, but the Greek peoples themselves. From mighty Ajax and Heracles to the wily and crafty Odysseus to the noble yet divinely faulted Oedipus to the creepy Antigone, the characters that populate the works of Sophocles are deep and complex. They are larger than life, individuals which are eventually brought down by a combination of their own actions and the unyielding will of the gods.
His plays are not as long as most of Shakespeare's, so they are easier to digest in a single sitting. Even non-thespians and theater lovers would enjoy these works of art. (I'm not a theater person myself) If you only read one of his plays, read Oedipus Rex. It's by far the best play I've ever read or seen. It's worth the hour or two to read it, as are the rest of his plays.