Hello and welcome Fudge
I had my first DC at age 37, this will be my second at 42. I went to 40+6 last time and then had a natural labour (started by waters breaking when I was crawling about trying to fix the Sky+ box - I recommend it!). Quite a quick Labour with just a tens machine for pain relief.
In the intervening period I have been responsible for a high-profile maternity unit and so I have got to know a lot of obstetricians personally and have been exposed to how maternity units are staffed, manage risks and incidents etc. The unfortunate consequence of being a senior manager is that only the concerns and incidents came to my attention (no one ever recounted 'normal boring' deliveries to me) so I ended up with quite a skewed view on the risk of childbirth! I know that in reality it is almost always fine but ignorance was definitely better!
With regards to your decision Fudge I will only say re. Staffing that there will not be 'no doctors' at 3am. Worth asking your hospital what their out of hours arrangements are to. E completely reassured but in my place ward midwife staffing ratios are the same 24/7 (apart from management staff who tend to work office hours, also more admin during the day because that's when all the planned admissions happen). Medically there always has to be a duty consultant ON SITE, as well as registrars. All the departmental consultants take turns at being on call on a 24/7 rota so you are as likely to get a 'good one' at night as during the day. There will also be an emergency theatre team on site out of hours, on standby for emergency sections. In my old trust (quite a big one) this was completely separate from non-maternity services, ie that's all they were there for, no burst appendixes or whatever. I would expect that to be the norm. Also always a theatre kept free and ready for emergency Caesarians.
I am not trying to persuade you one way or another, just hoping to allay your fears about people being on around and on standby! There are certainly more people around during the day but many are busy in clinics and with scheduled work so for a crash section it is always the duty consultant and emergency team (assuming you are having an NHS delivery). Also, if it reassures you further, Labour is a properly round-the-clock process as many women Labour at night naturally, so they are not 'ghost towns' like other wards can be! I turned up at my local hospital at 4am to have my baby and the place was heaving.
My approach last time was that I wanted a natural delivery (for a quicker recovery time) if possible but was very open to whatever was required and recommended. What I really didn't want was an emergency section, for the reason of it being v stressful and scary (obviously!) and because if you haven't got an epidural in already they tend to need to give you a general anaesthetic for speed, so you'd be asleep for the birth. Hence, if there was any reason to be concerned about the delivery (due to baby's position, for instance) I would opt for an elective section but if not I would go for natural. That was my approach last time, same this time.
I would recommend you get views from the consultants and midwives (who each have different perspectives) and then do whatever you are comfortable with, and try not to feel pressured (easier said than done, I know!)