Can see govt hospital as subsidised patient for the first 20 weeks, after that it’s better to choose a gynaecologist as private patient (be it govt hospital or private hospital) . But do note that subsidised patient means you see random doctors every appointment. Unless your pregnancy is high risk or many complications, then you should choose gynae from the start.
if cost is a concern then just go with subsidised route but you won't be able to choose your gynae.