I would really caution against 'picking someone and not telling anyone' as far as setting up guardianship for your children goes. Look at it this way; you goal is that should (God forbid) anything awful happen to YOU that there be as little ongoing conflict about who cares for them as possible. If you don't talk to people about it before hand, they're more likely to freak out when they DO find out, and you're more likely to have a court challenge. And you are correct that at least in Wisconsin, if a gaurdian can't be found for minor children they'll go into state care until the court can appoint someone -- ususally, it's a really short procedure, but only if no one is contesting the guardianship and making a fuss.
Also, there are legal limits to what kinds of decisions you can specify when you're setting someone as the guardian of your children, since there's only so much control you can have from beyond the grave. If you're thinking of a complicated scheme with joint custody or something, see a good family lawyer and talk it over with them first!
Also, it's not always the best idea to specifiy who you want to be your children's guardian ONLY in your will bcause a will is only read after you're dead, sometimes days or weeks after-- what if you and your DP (again, God Forbid!) were in a catastrophic car accident and were seriously injured but not dead, but your children still needed day-to-day care.
My humble opinion (with the standard disclaimer that I'm not a lawyer, only a wanky law student, and so this should in no way be considered actual legal advice) is that a durable power of attorney for Health Care and Finances is SOOOO much more important than a will. The state has ways to handle guardianship and property when there is no will, but does not have good ways to handle health care decisions and decisions about finances without a legal document. Also, although all of us will die, hopefully most of us will live to a ripe old age and not die while we have minor children. However, nearly all of us have the potential to become incapacitated, even for a short time -- fall and hit our heads, serious illness, car accident, whatever -- and need someone to make health care decisions for us. Your Powers of Attorney are far more likely to be needed without advance warning than your will!