What Can Be Given by The Law of Surprise?

It can be anything.

Anything that the person first finds at home which he doesn't expect to be there.

Of the price of a man who saves another can demand, of the granting of a seemingly impossible wish. 'You will give me the first thing that comes to greet you.' It might be a dog, you'll say, a halberdier at the gate, even a mother-in-law impatient to holler at her son-in-law when he returns home. Or: 'You'll give me what you find at home yet don't expect.' After a long journey, honorable gentlemen, and an unexpected return, this could be a lover in the wife's bed. But sometimes it's a child. A child marked out by destiny.
_{The Last Wish - A Question of Price}

Most of the famous examples of the Law of Surprise involve a child surprise. Especially so in the case of witchers, who invoke this law in the hopes that the person they saved comes home to be greeted by their new-born child, which the witchers can then claim and train as their own.