Then, definitely, cheapest sturdy, waterproof watch you can find, one you wouldn't mind getting broken/destroyed. Check your school's dress code policies -- most schools require a watch with a sweep second hand.
I've been wondering the same things since I start clinicals in a couple of weeks. All they said was a watch with seconds, that is waterproof, and we have to take it off every time we wash our hands (?). Non-nursing, I've had great luck with the 10 dollar wal-mart or target digital watches, kind of like the link above. Each one has lasted for at least a year of daily wear during the evening, when I sleep, go swimming, running, to the lake, etc.
Yes anything that is cheap and digital is a great way to go. Schools will tell you that a watch with a second hand is the way to go, but doing VS or anything else can be done with a digital watch. I have always bought cheap timex digital watches. Anything cheap and plastic will help out. I have tried metal bands, but they rust; fabric bands, but those smell and are hard to clean; and leather, just forget that...they are a bare to clean, and also get to smelling. Plastic is great as it is cheap and can just be tossed when really dirty, or the paint starts coming off.
I'm a guy with some fat wrists. I got a G-shock, and I love it. It's easy to clean, easy to read, and it has a lunar chart so I can call out when it's full moon! G-shock has a great reputation for quality and great reviews.