Which is usually older, stalagmites or stalactites?

Answer 1

Neither.
They form at the same time, and through essentially the same process. Highly concentrated water drips from the ceiling, leaving mineral precipitates behind. It then falls on the floor, leaving more precipitates behind.

Technically, I guess you could say that a stalactite STARTS first - while the drop is still in contact with the ceiling. But only by the duration of a single drip.

Answer 2

stalactites are the ones on the top and form before the ones on the bottom