Private or subsidised route

Hi all, FTM here, just tested positive and is around week 4 now. Not sure what to do from here onwards and if private or subsidised route is better(in terms of waiting time etc) have been thinking of subsidised first then change to private too, but am not sure how's the procedure like. Would love to read some experience from fellow moms here! Thanks in advanced! #adviceplease #firstmom #newmom