I had similar concerns as I had not visited the USA since April 2000. Got to say passing through JFK was painless. Took one hour to go through Immigration and I was last off the B744! At Immigration, your photo is taken with a 'web-cam' type device and you are finger-printed (index fingers). Thankfully the finger printing is electronic; I had visions of old fashioned black ink!
Remember to fill in the green visa card properly as I forgot the reverse. Top tip, if you are a Brit. your country of origin is 'UK', not England, Wales, etc. Thankfully the BA CSD told us this on the aircraft, so top marks!
After Immigration, there was a few questions from the Customs officer, "are you bringing more that $10,000 to the USA?". I wish (!) but answer sensibly! You are asked if you are bringing 'food' or 'meat' into the country as well.
As mentioned above, took one hour. Don't joke with the officials, be polite etc. I also submitted my address in the USA when I booked my ticket online to cut down on possible hassle. Needless to say, BA having a dedicated terminal at JFK helps; can't comment on other airports in the USA. By the way, no hassle from the TSA on the return leg either.
As for the passport, it has to be machine readable but as I had a new shiny one from the British government, I had no concerns.
Lastly, if you thought the flight-crew escape this process, they don't! Hope this all helps.
