I call slalom the violent discipline.
I usually tell people to invest in pole guards, then a chin guard, and finally shin guards. Whack your fingers, and you'll want the pole guards. Miss a block and take a gate to the nose, the chin guard makes sense. Take a series of gates without shin guards, and you'll understand their utility- especially the next day. As you move closer to the gate, each gives you a little more confidence and protection.
Padded gloves and jackets are nice, but not required.
Of course, I know plenty of skiers that don't use guards of any kind. I've done it on occasion, but I wouldn't recommend it.