i just have both on mine for extra protection

Same here. And while I had never gotten a screen protector before (never had a touch cell phone before either), I've always gotten a case w/ carrying clip and highly recommend it for those who don't always put the phone in their pocket but rather just clip it to the belt.

So, in general, I'd recommend getting a carrying case and at least the external screen protector. The internal screen protector is not really necessary. If you don't get a carrying case, then maybe you can get the full phone plastic protector (like the full InvisibleShield), but I don't have any experience with that.