As an American you are subject to income tax on your world income each year and must file a US tax return if you make over $8950 if single or $17900 if MFJ(note these amounts change each year). You will get a foreign income exclusion if you qualify.
As for selling your residence in Poland when you move to the US, the gain would be not taxable if you qualify for the 2 out of 5 year rule & the gain is $250000 or less if your single or the gain is less than $500000 and you file MFJ and both of you qualify for the exclusion.
The 2 out of 5 year rule: You must have owned & lived in the property as his or her main home at least 2 years during the five year period ending on date of sale.
