Both my first two were 'normal' births. My third was a prem. I had an infection which caused labour to start at 31 weeks, almost 19 years ago now, so info might be slightly outdated.
C-sec or normal delivery depends on baby really, so I can't comment on that.
I was given some meds to try and stop labour, and injections to mature her lungs. Labour stopped for about a day but started up again towards the end of the second day. I was given Pethidine to help with the pain, a light fell off the wall on to me!! and when I said the baby is coming they didn't believe me. It was then panic stations, a incubator was brought into the room, there were a lot of medical professionals about.
After she was delivered, she was taken away, and I presume put in the incubator and taken away for what felt like forever, but prob about 20 mins. They brought her back in all tubed and wired upand then whisked her off to NICU. They too a polaroid photo of her for me to keep, and I was taken to the ward where I was to stay. That was one of the hardest moments. Being on a ward with lots of new borns and I was the only one who didn't have her baby. I did get some looks.
NICU let you visit when you want, but sometimes they need to do procedures which they prefer you to go to the visitors room for. They do like it when you can help with the care for your baby, and encourage it when the time is right.
One of the best feelings and scariest is holding a prem baby. So so small. Mine was 3lb 10ozs.
I expressed milk when I got home and froze it so she could have my milk. Borrow a machine from the hospital if you can. Much more efficient than the ones you can buy. Or at least they were 19 years ago.
I wish you all the best OP 