Hi, congrats. Typically, at your first visit, you will need to take the urine test, do a vaginal ultra-sound to assess the progress of your pregnancy and expected date of delivery (EDD). Your gynae will also speak about any discomfort that you are facing like morning sickness, nausea, etc. and if everything looks like ie. the gestation sac is right size, at about 6 weeks, heartbeat is detected, then he/she will share about subsequent appointments and what to expect like OSCAR test at Week 12, detailed scan after Week 20 etc. The nurses will also explain about the prenatal package.
Your choice of gynae may affect the hospital coz some private practice only deliver in specific hospitals. I think in general, hospitals are quite comparable except for the prices difference. There are some threads discussing gynae and hospitals in this forum, you should take a look.
You need to be comfortable with the gynae and prioritize your preference. Good Luck!