Antioxidants sound to me like an investment that's best made the earlier the better. Will it make any significant impact if I start taking them at 60 years of age?

As with so many things that are good for you, it is certainly best to start as early as possible. However at any age you can still reap benefits from antioxidant protection. If you have looked after yourself for the first 60 years and start taking antioxidants now, then there is a good prospect of your next 60 years being healthy and fruitful!