Answer by Bob Watson:
An introductory flying lesson is about as safe as they come. The lessons that lead up to a PPL are all going to be done with safety foremost in mind.
A light plane that is being used for flying lessons is inspected by a licensed mechanic every 100 hours of operation (about every couple of months) at a minimum. The flight instructor you'll be flying with has more than a hundred hours of training and many more hours of practice (often many, many more).
Enjoy your flight!