Congrats!! I love how you are such a hands-on hubby. So rare!
I saw 2 docs before I decided on the doc that I wanted. First appointment the doc will do a scan, it can be a vaginal scan, so they can see clearer images. You will see your little bubs inside and also hear the heartbeat. I am delivering this year, 38 years old. First baby. So I was kiasu and went to the polyclinic to get a referral and got the subsidised route to KKH. In the event there are any complications, I will fall back on the subsidised route, so will not be so expensive. Whichever doctor you choose, most important thing is that you and your wife need to feel comfortable with him/her.
After reading the forum pages here, I went with Dr CK Khoo at Mount E Novena. He was the 2nd doctor I visited. The first one I was not so comfortable.. her nurse very fierce. haha. Dr Khoo used to be a KKH doc and came out to set up his own private practice. My first visit, he told he he has like the record number of births done at KKH. So I guess he has seen almost everything ald. I think he was also in the news last year for delivering twins to the oldest mum in SG. He's very friendly and approachable, super chill kind of doctor, will spend the time to sit and talk with you and explain things to you. I feel I can ask him any kind of question and not feel stupid, haha. Some of the more popular doctors can't give so much time to each patient. He's pro natural as well. I kept asking him at my age if I will have any complications, and he assured me that he won't get me there. When he found out that I was at KKH subsidised, he also advised me to do my scans there, then just bring the result back to him, to save me some money.
Some of the things you can find out at your doctors, if they offer packages. Quite common for them to offer packages in the 2nd trimester. Because of COVID, doctors can only deliver at 1 hospital unlike before, so you will have to be ok with the hospital and the costs at where your doctor delivers. You may want to check on the hospital charges too and what freebies the hospital gives to the mamas. Also the costs of the tests/ vaccinations that you need to do at each milestone. These are usually charged separate from the package/ consult fees.
Also, it is useful for your wife to join the Whatsapp groups for mamas that are due in the same month. I found it very useful as a first-time-mum. Or do a search on FB, join the Mummies-to-be FB groups. A lot of people share information there.
All the best!