Choose your hospital first. Look at where it is , traffic to get there, their policies on baby rooming in, Caesar policy on skin to skin; are there lactation consultants on site that you can see; is there are special care nursery or a NICU? If not, where would baby be transferred to if they need NICU.
You can call the Hospitals and ask these things if you can't find the info on the web
Then look at the OBs that deliver there. Do you want a female/male; look at whether their rooms are on hospital grounds or elsewhere; so how easy will it be to get there for appointments; what about parking.
Once you have a shortlist Ask for recommendations here or google their names Then call their rooms and ask for their fee structure and mention that you want a caeser if you want to be certain they .
Most private OBs will work with you. They'll lay out risks and benefits and plan your elective at the best time medically