My parents recently tried to remove the popcorn ceiling that's been in their house for the last 20 years. The entire house, except for bathrooms and kitchen, has the stuff, but they decided to try just the dining room alone, first. If you thoroughly wet the stucco (you can even use a squirt bottle for this), it practically falls off. Trouble is, as SQLit mentioned, it's a huge mess, and the resulting ceiling is rough. And, working on a ceiling is a serious pain in the neck.
For my parents, they decided to stop after the one room (they'd had enough), did a quick job spackling imperfections, and are now painting it with a faux finish texture to camoflage the flaws.
They decided to do all this stuff themselves (they have always been do-it-yourselfers, but they were hesitant to tackle this project) because the cost of having it removed was so high due to a special hazardous materials charge after trace amounts of asbestos were found in it. Since your house is new, I don't think you should have any asbestos, and the removal cost may not be too bad.
Oh, also--the stucco is easier to remove *before* the first time it's painted. And as far as painting goes, are you planning on painting it a color? If you are painting a color significantly different from the existing white, you are in for some major work getting it into all of the nooks and crannies. Even with hwm's suggestions, in my experience, it will take many passes to get a roller into every crack, and spray opens up a whole new ballgame as far as mess, etc., especially for the inexperienced.