A typical and fairly formal one would be "Go-kou-un wo oinori-shimasu."
If this is between adolescents, this would be too rigid and formal, but I don't know how they would say it, ..maybe they don't say something like this each other. At the time of farewell, they would say "Genki-dene", literally "Stay healthy."
Should you translate it without any context it will turn out like あなたの幸運と幸せを祈っています。(lit. I'm wishing for both your good luck and your happiness), but when it comes to stricter and politer one, it might differs a bit from the above one: for example, ご健勝とご多幸をお祈り致します。 which often appears on an E-mail.
Because we are dealing with ideas always and not with facts we have remained with dilemmas, conflicts and so on leading to unhappiness. This sense of unhappiness breeds a longing for happiness and hence it is a vicious cycle, one chasing the other.
The amount of good luck coming your way depends on your willingness to act. Good luck is a residue of preparation. A great man's greatest good luck is to die at the right time. It's hard to detect good luck - it looks so much like something you've earned.
It can be used in professional or informal writing. It invokes a sense of kindness that you are wishing them all the best, but it's shorter than saying "I wish you all the best". Use this if you don't need to be overly formal and are ok with more of a relaxed tone with the person you are emailing.
Introduction: My name is Nicola Considine CPA, I am a determined, witty, powerful, brainy, open, smiling, proud person who loves writing and wants to share my knowledge and understanding with you.
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