Which way to use when moving a player?

I’m trying to make a game with a tower where blocks stack up. The blocks come slide in and when the user taps the screen the block should stop. But If the tower is to oblique the tower should fall. So I need a rigidbody on the blocks, but how do I then slide them in without letting them fall to the ground(because of the gravity)? Sorry for My bad Explination and English. Help would be very appreciated!

This: link text is what happens when I use transform.Translate. But I want this: link text with gravity. What should I use? For example: transform.Translate, Vector3.lerp etc.