Congratulations on your pregnancy! Boy? Girl? Multiples? Not saying yet? We moved here about 2 months ago when I was 17 weeks pregnant.
My suggestion is to pick an OB first and then you can figure out the hospitals. I am seeing Dr. Dawkins as my OB and he is fantastic! I had to see Dr. Ferguson once while Dr. Dawkins was away, and she seemed wonderful as well. They are both very caring and attentive.
One word of caution with your medical insurance, please check to see exactly what they cover. We were told our insurance covered all maternity as well... only to find out when we arrived that we are only covered for HK$6000-9000 (600-900Euros) and that is including ALL prenatal checkups with the private Dr.... so, by the time we get to the hospital, if we choose a private, it will be mostly out of pocket which is very expensive. Hopefully yours does cover everything. That would be great.
Once you become a Hong Kong resident, you are covered by the public health system here... which, if you read some of the other strings from this forum, you will find that the Dr. and nurse care at Queen Mary (pubic), for instance, is excellent. The rooms and food may be a bit lacking from what I am told, but the care is very good. Just make sure if you want the option of using a public hospital at public fees, apply for your resident card as soon as possible.
We too will be choosing an elective c-section (because I am pregnant with twins) and after discussing with many mothers and reading up on these great forums on geobaby, we will most likely decide to go to Queen Mary for the delivery and only use Dr. Dawkins as a private OB up until that point. Otherwise, if we choose private, we will use Matilda, and be ready to pay a huge bill at the end.
Depending on who you choose as your private OB, I believe they are individual as to which hospital they will deliver. For instance, Dr. Dawkins delivers at Matilda. And private Dr.s, I have been told, cannot deliver at the public hospitals.
These are things I have learned since I moved here. I hope it helps. I really found that once I settled into my OB, I was able to start investigating the hospitals.
Best of luck! If you have more questions let me know, or private message me.