Is writing the Quran by hand a good deed to draw closer to Allah, or is there a better deed from which people can benefit?

You have done well in focusing on what brings you closer to Allah. Printed Qur'ans are sufficient and spare you the need to write a Qur'an by hand. We advise you to occupy yourself with instilling the Qur'an and knowledge in the hearts of the young, for "The best among you is he who learns the Qur'an and teaches it."