Bit of a consensus on this one. Private room. No question. You've got the rest of your live to chat to random strangers about your baby.
I spent a lot of my pregnancy in and out of hospital and before I sussed the private room situation/medical insurance was stuck on a six-bed antenatal ward for five days at a time. It was hell on earth. No sleep from bleeping monitors, shrieking women and, memorably, one woman who spoke not one word of English and insisted on leaking her amniotic fluid and blood all over the carpet tiles rather than the bed - driving the midwives mad and leaving us all with a room that stank of an abbatoir for days afterwards (and no, it didn't get cleaned, unless you count me pinching a bathroom cleaner from a cupboard and spraying the area).
I had a private room and it was the best thing I ever did. My own en suite bathroom (the loos for the shared wards were a Hammer Horror gore-fest and the shower cubicles were covered in coils of hair and blood and shit) and fridge and peace and quiet. Not having the nurses in yelling distance made no difference to me as I had my buzzer and my experience of the ward was that you could yell all you liked - if they were too busy/couldn't be a*sed to put down their book (Cecelia Aherne was obviously a gripping read!) you weren't going to be looked after.
Private room meant no one else's visitors, noises, babies screaming, food smells. I had peace and quiet and a window I could open. I spent the last month of my pregnancy in the hospital at the end and I used to walk around a lot to alleviate the boredom and I'll never forget the noise and smells from the ward - babies shrieking, mothers crying, water jugs not replaced. Equally, visiting friends when they had their babies and were on the wards and they were desperate/begging to leave.
Get a private room if you can. If you find you hate it and you want to move to a ward the odds are they'll be able to move you over pretty quickly. Someone would probably gladly swap with you!!
Best of luck.