Hi hi, i can understand why you have mixed feelings. I knew i got pregnant when i am due for promotion and have a lump sum of money waiting for me after serving for some years and i have to give them up because of my weak health during pregnancy. However, being pregnant and knowing your baby is inside you is a joy beyond all things. Maybe try talking to your boss to have a change of duty?
I think it is better to visit a gynae once you know you are pregnant. As for which gynae, I guess you can check the forum under 'Singapore Obstetricians and Gynae' for recommendations of any good gynae nearer to your place. I think it is better not to sign up a package first until you are comfortable with the gynae looking after you. Once you are ok with the gynae, signing up a package is usually cheaper. Some gynaes only go to certain hospitals so i guess you have to look for your gynae first? Sorry that i cant reco. you gynaes or hospital cos i also a first time mummy. Hope what i have suggested is of help.
By the way, congrats, welcome to motherhood and enjoy your journey of pregnancy.