There is actually a special arrangement for this. You first select the whole text box and select the animation you want (like "Appear"). Then you open the animation pane and click the little arrow on the line that represents your animation for the whole text box. Click "Effect options..." and then go to the "Text Animation" tab. In the "Group text" list select you preferred option (probably "By 1st level paragraphs") and the Ok.
Hope this will help!