my wife and my two kids. ?
Where are you from (citizenship)? What do you mean by IT guy (education, qualifications, experience)? How old are your kids? Does anyone have special needs? What kind of lifestyle to you expect to lead? Without this information, it's well nigh impossible to answer your question with any degree of accuracy.
In general, though, you're probably going to need about 11,000 PLN net (after taxes and deductions), or about 17,000 net. You're not going to get that much unless you are a very experienced SAP or HBase consultant, or similar high-level technical specialist. Or a high-level senior administrator or top level manager. Any less and you are going to reduce your ability to save up any substantial amount of money for a rainy day fund.
Housing is going to cost you about 3000 to 3500 pln all inclusive (rent, maintenance fees, utilities, phone, internet, cable and heating).
Food and basic household supplies at least another 1500 PLN.
School for two kids can easily set you back 2000 PLN a month for a good private school.
Entertainment and travel are a huge wild card.
Make all plans on the very safe assumption that neither your wife nor your kids will be able to earn a single penny during your whole stay.
Also take into account that, if your wife has a career, she will have to put it on hold for the duration of your stay, and unless she speaks Polish, will have very little opportunity to enhance her credentials or qualifications.
Also, take into account that your wife and kids may be quite isolated. Most Poles do not speak English, and even people in their thirties generally do not beyond a basic level that may not be good enough for free-ranging conversation.
If you are from India or Korea, remember that those expat communities are extremely closed and rigidly stratified, so if you are not in the "in crowd", life can be very lonely.
Last of all, unless you are a top level administrator or manager, remember that the location in Poland is dedicated almost entirely to outsourcing or insourcing, and that you will be cut off from the mainstream of the corporate culture (basically, it's like being in the windowless basement). That can greatly reduce your opportunities for advancement.
Working in Poland can actually close more doors than it opens. Make sure you talk it over with several people from your country who have done it before (face to face, not on the internet).