First, Californian laws says that you must have a legal precence document from the issue of the driving licence valid for 60 days. I went to get my driving after about 60 days of my arrival... and then my K-1 was valid only for 30 days more and I still hadn't applied for green card. So in principle they shouldn't have to issue me driving license at all. But they did and I was contacted from DMV and asked to come back and issue a document about my legal precence. That was after I got my EAD and they accepted it as the legal precence document.
So what this means? I was lucky... I wasn't in fact eligble for driving license. This means that go get your driving licence immediately after your arrival. Then your K-1 is still valid for 90 days and you are eligble for driving license. This is situation in California and I have heard that in some other states they don't require a legal precence document at all.
Another issue in driving licenses is that they only issue you temporary driving license. It is going to be valid for 3 months and they should send the permanent (for 5 years or so) card in that time. But this doesn't work for aliens. It might take longer than 3 months to get clearance from INS. But this is not a thing to worry... just go to DMV and ask extension to the temporary license. They stamp it 60 days extension and sometimes you don't even have to wait in long lines for hours: information desk ("Start Here" desk) did it for me when I asked where should I go.