Yeah, definitely buy a protective case for it, preferably one with a screen cover. Some products have hard plastic covers; others have a thin, sticky film you lay over the screen. There are a plethora of brands with a plethora of styles, but you'll definitely get your best selection by going into your local Apple Store.
Also, the screen is made of a surprisingly solid material, but it can still scratch. Try to avoid keeping it in the same pockets as keys or other abrasive materials. I've got two little knicks on my iPod from before I got my case for it, and I always thought I was pretty careful with the thing.
Don't ever, ever get it wet. Try not to even leave it in the bathroom with you while you shower or anything like that, or the moisture can affect the board or affect the headphone port, and service providers can tell right away if there's been 'spill' damage and usually make you pay for it.
Also, get the APP to extend your warranty to 3-years. As long as you don't physically break the phone yourself, it will cover any other hardware failure the phone could have. And for Apple, it's usually more cost effective to just give you a new phone if your old phone breaks.
The damn things are addictive. I've had mine about a year now and I still have to be told to put the thing away and pay attention on many an occasion