You do not HAVE to deliver where the doctor has his/her practice. The doctor who delivered my baby has her practice at Gleneagles but can also deliver at Mount Alvernia, Mount Elizabeth & Thompson. Same is true for the doctor I visited at a Thompson Medical practice - He would also deliver at Mt. Alvernia. You just need to check which hospitals they can practice.
That being said, I think it is more convenient to see the doctor who practices at the hospital where you will be delivering.
What is very important is to have a good relationship with your OBGYN - and feel very comfortable and in capable hands. What appeals to one person may not appeal to you - so best to get recommendations and see who you feel best with.
(*edited to include: sorry bruinbear - i think i basically just seconded everything you wrote
)