I had an emergency cs rather than a planned one, but it was pretty much as others have described (but rather more rushed!)
The anaesthetist ran his hands up my tummy to make sure that the epidural had worked, the screen was put up, I had a heart monitor attached to my finger then my hands were strapped up into the top of the screen. I didn't actually feel any kind of sensation at all - no tugging or rummaging, although I had been told that it feels a bit like someone is doing the washing-up inside your tummy! It only took a minute or two to do the cutting and delivery.
Once dd was lifted out they held her over the screen for us to see (although I couldn't see her - but dh could), took her away to check her over and clean her up, then brought her over for dh to hold, although I wasn't allowed to hold her at that point. My dh then took her away to dress her while I was stitched up, and I was then wheeled into the recovery room where dd was given to me and I fed her (I can't remember that at all). I was hooked up to bp monitors, oxygen, a drip and a blood transfusion, so I was monitored for a couple of hours before going back up to the ward.
I would say that the worst thing for me was not being allowed to hold dd until I was taken out of the theatre, and the fact that although I can remember seeing her when she was given to dh, I can't remember the first time I held her and fed her. If I had to have a section again, I would try and ensure that the baby was given to me as soon as possible, and not taken away while I was being stitched. Looking at other people's stories that's not standard procedure, but it might be worth you checking whether that's what your hospital do.