Depends on your finances too. I went the subsidised route first before switching to private (after second trimester in the same govt hospital). Hospital referrals from polyclinic for the first appointment definitely takes longer.
If you are considering public hospital and dont mind team-based consultancy (meanig you see different MO each visit), then you can go to a polyclinic for a referral letter to public hospital as a subsidized patient.
Chathz Ku