I have been offered the position. I have already filled out an ETA 750 and an I-140. But I found out later that an I-129 is what I should have completed. Non-immigrant status is relatively fast to obtain. The waiting time is measured in months.
Immigrant visas take many months or even years to obtain.
My wife is a US citizen. She sponsored me for my green card, which I have just obtained. She also wants to sponsor her parents on immigrant petitions. The green card is valid for entry purposes if you have not been outside of the US for more than one year. That being said, INS can try to take away your green card by claiming you have abandoned your residence even though the absence is less than one year.