In my experience it is very easy to register, you just need to take ID along. Either passports (initially) or local ID cards when you've had those issued.
Meds are pretty tightly controlled in SG, from my perspective. Some things you can get over-the-counter back home you'll need a script for in SG. Some meds are very expensive in SG (again, my perspective). One recent example I had was antibiotics for a simple ear-infection, and the course cost something like GBP70. Added to which they didn't resolve the issue so I had to repeat the course at a higher dose => those 1gram horse-pills were even more expensive.
If possible come with a good supply of your own meds. For example if you arrived and visited a private doctor (still technically as a tourist) downtown then it can get expensive. BTW what if any local health insurance are you expecting from the employer? Once you find a place to live then register with a doctor who is convenient to get to. The doctors surgeries often have their quals (what and where from) and any specialities listed in the windows. Example: a doctor who graduated in an English speaking country might be considered almost a necessity, especially if they're going to be the family doctor for a few years. Being able to 'speak your language' is not simply the words, perhaps especially with the subtlety of medical symptoms etc., it's understanding the nuance beneath them. So having a stroll around the neighbourhood and looking at such windows, and word of mouth at where you're living is a simple way to narrow down the field.
[If it would help at all I can recommend my dentist. I was impressed with her work, and since she graduated from Bristol, near where I grew up, there was an immediate element of connection and trust. She's downtown, but dropping by there once or twice a year could always be fitted around other things I had to do down that way so it wasn't a problem for me).
One thing you might consider re: your GP now... have you asked him/her what is the maximum duration prescription they can write? If you were planning a trip home say once a year, then could they write you a script to last you a year? That would be sooo much simpler and cheaper for you. Or could they write a repeating-script that a family member could periodically collect and forward on to you?
Re: eye-correction. Yep SGns must rank no.1 in the world for wonky eyes as I've never seen so many opticians in any other country. Mind you the same applies for mobile phone shops - maybe they spend too long squinting at their phones?
Eye-adjustment in SG can be very good value for money. In fact it used to be something of a pro-tip for tourists from Europe to bring their prescription with them from home, and have supplies made up whilst on holiday in SG or Malaysia. It can be waaay cheaper than back home. For example I started wearing reading glasses a few years back. I dropped into a local optician and they gave me an eye test (by a qualified (in the UK as it happens!) optician). Then I chose the frames, decent looking but non-designer/fancy/branded. They cut the lenses to size, retested me in them and with the box and cleaning cloth + a mini screw-driver and some spare replacement micro-screws that came to S$138 - about 70 pounds.
Welcome to the forum!
p.s. I have a friend in Guernsey, I expect you know him [lol /jk
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