My 2 cents: I have Littman's top of the line stethoscope, and would not recommend it--not because it is not good, but because it's heavier, and frankly, way overkill, despite what advise you might get to "buy the best you can afford" or "you need something that you can really hear every nuance in heart sounds". For a floor or clinic RN, you really don't need anything more than something that can hear crackles and wheezes in the lungs and irregular heart sounds. Even cardiologists that often visit our floor don't usually bring their own stethoscope and they don't go seeking out a "really good stethoscope" to check on their patients. Really, my experience has been that you need a stethoscope that lets you hear as good as it can for being as light as it can be, because you'll carry it for 12+ hours around your neck or wherever, unless you'll be working in an 8 hour shift environment. Having said that, we have disposable stethoscopes in our isolation rooms, and they are really a pain to try to hear anything at all. We call them the "toy stethoscopes", and they really are about the same caliber as what you might find in a toy store. But if the room is quiet, they get the job done.
Shoes, I've found, are a very personal choice item. You just have to find that works for you, because I've seen, on a number of occasions, one nurse raving about a shoe, another nurse buying that same shoe and hating them. For myself, I just have a pair of good running shoes. Mine happen to be New Balance, but there is nothing magic about that.
I would, however, suggest knee high support hose. I went from feeling like my legs were bruised by the end of a particularly brutal shift, to feeling like my lower legs were the only part of my body not feeling tired. You can get them at Walmart for about $15. I tried to get a prescription and my doctor gave me the runaround. After talking with another doctor, she confided that doctors really aren't taught how to specify a support hose strength, and that was the problem with my doctor. She gave me a script but the medical supply store wouldn't fill it without a strength specified. They finally gave up gave me the wink-wink direction to get them at Walmart--it's the same as what they sell unless you're getting a particularly strong compression.
As for lights, I do have a small LED light on my badge that I use, but if I don't usually need it, and if I do, I prefer the penlight flashlights that have a more natural light, but it's not strictly necessary.
I like Cherokee for scrubs brand, but only because they have lots of pockets. The fabric has held up to many washings (nearly 3 years on this set, but I rotate throught 4 sets, so consider that), but they workmanship on pockets is not good as nearly all of them have come unravelled and had to be mended.
I recently bought some 4" bandage scissors on eBay and they were cheap and work well for cutting any number of things, including dressings that need changing. I just wipe them with the super antimicrobials when done.
A Sharpie or other permanent marker is nice to keep for marking lots of different things, including medication patches, paper tape that you use to mark tubing, dressings, etc. I like what our hospital provides, which is the type of permanent marker that works like a retractable pen (clicker).
As for a watch, it doesn't matter if it's analog or digital. You just need something that count off 15 seconds for taking pulses, measuring respiration rate, etc. I like the idea of the little dials that click off 5 second increments, so you can get started within 5 seconds and just watch that increment 3 times, but I've never actually had a watch that does that. Really, any watch will work. As for "soiling", I've always just had a waterproof watch that can be cleaned with soap and water, although it's usually covered by my scrubs and rarely gets dirty...
We never had to buy a gait belt in school, but I wouldn't waste much time researching or anything. Get something that will get you through school. All of this agonizing over what you need will be a distant memory soon enough, and you'll have that "RN" by your name and you'll be "living the dream", as I always say sarcastically on the floor. Having said that, it really is a great field for the young. I regret changing careers in my late 40's, but may change my mind if I get out of the nutty acute care setting. It's a lot crazier, but it's a great foundation for your RN resume. Good luck!