I'll do my best to answer your questions, but it would help to have some more information:
Where should we stay? If this is your first time in Prague and you will be here for three days, then I would recommend staying in Stare Mesto (Old Town), Mala Strana (Lesser Quarter), or possibly Nove Mesto (New Town). These neighborhoods are in the center and are among the prettiest parts of Prague.
One good place to look is Mary's Apartment Agency, which has basic, central apartments for good prices: www.marys.cz
How much money do we need per person per day? I apologize in advance, but there's no real way for me to answer this question. It depends on what you want to do while you are here. Some basic prices:
US$1 to 1.50 - half liter of beer in a pub $10 to $15 - price of a decent meal in a decent restaurant in the center (including a couple drinks) $1 - price of a metro/tram/bus ticket valid for 75 minutes
Entry to sights isn't too expensive, with many things available for free. Shopping here can be quite expensive, especially for electronics and things in the new shopping malls. These types of things are more expensive than in the States.
Basically, if you are on a budget, there are plenty of cheap options in Prague, in many cases much cheaper than budget options in Western Europe. But there are also a lot of things here that can put a hole in your pocket.
Is three nights enough? Well, it's a start ;D It's definitely enough time to see the major sights and get a decent feel for the city center.
Will I also want to live there permanently once I have visited? That's what happened to me ;D
Have a great trip! And if you have any more specific questions, just let me know. I'll do my best to answer.