Liability insurance - get it ASAP. Most policies will also cover you for things you do when not at work like giving advice to friends, taking BPs at the local church , etc. I have heard that the best policy to get is a policy that covers you for any lawsuit that is brought against you during the time that you have the policy. So if if you buy the policy and keep it, in a couple of years if someone sues you for something that you are going to do tomorrow, the policy covers you AT the time the suit is brought, no matter how long ago the incident occurred. Do not count on your employers insurance to cover you. If it is in your employer's best interest to hang you out to dry, they will do it.
Work related items are tax deductible if you are not reimbursed for them by your employer. Includes uniforms, shoes, stethoscope, nursing conferences, CEUs (even homestudy), nursing association dues, nursing magazine subscription. You have to keep all your receipts. You will also have to itemize your tax return. If you do not have enough itemized deductions than you will have to file a "regular" return. So you will need to keep any and all receipts of anything that could be deducted to help you have enough deductions to qualify (you have to spend a certain percentage of your income on qualifying items). You can deduct things like home property tax, mortgage interes paid, money spent on health/dental insurance, money spent on doctors, on medicines - those are some of the biggies. If you don't own a home and don't contribute large sums to charities, chances are you won't have enough deductions just from your nursing receipts. But it doesn't hurt to keep the receipts and add them up at the end of the year and see what happens. An easy and fairly cheap way for you to learn about what you can/can't deduct and how much $$ you have to spend on deductions, is for you to do your income tax yourself this next year using a computer program. For about $30 you can get the program and it will walk you through how to do your return, what is acceptable, etc. Then you can learn about it while not paying an accountant.
While you're learning, just save all your receipts. I use a big brown envelope marked "Taxes - 2007". We put our paystubs, receipts in the envelope as soon as we bring them home. Then the receipts are all in place to do the taxes. Just start a new envelope every January first. Then you won't spend hours trying to find things you need.
Oh yeah - beware of employer dental insurance. Usually isn't worth it. You could end up spending hundreds of dollars a year to either never use the insurance or be capped at a limit, which is usually $1,000 per year. One root canal and a crown are going to cost WAY over a thousand dollars. It is usually better to put aside part of your check in a savings account or into a HSA or flexible medical account to use for dental issues.
If you have animals, children, or husband, life insurance is important. Especially if you have a mortgage and 2 adults in the family MUST work to make ends meet. Generally you should have enough life insurance to pay off what you owe on a mortgage, as well as any car payments. Then if you have kids that need to go to college, or kids/pets that will need someone to care for them if all parents are gone, you'll want money to provide for them. You can usually get cheap term life insurance from your employer that is good. If they have a life insurance plan that is portable, meaning it is group term life that you can keep even when you go to another employer, that is even better. I don't care for the "Whole Life" insurance policies. What they do is allow you to borrow against your life insurance policy to buy things. The insurance agent will tell you that it is good because you can borrow money to buy a car or an RV or something. What they don't remind you is that if you take $80K from a $100,000 policy and you die before you pay all the money back - your family does not get the full $100K. There also can be penalties and things that are hidden. IMO - you are better off with good term life, even if all you can afford is a $10K policy to give your family enough to bury you with. I know, not necessarily what people like to think about, but life insurance can mean the difference between your family being taken care of without you being around or being put out on the street.
That's about all I can think of that I wish I had known when I first started out. If I think of anything else I can let you know.