1. Do you both have a job n HK or only one of you?
2. if only one of you are you HKID holder or not
3. if not, and if only one of you has a job then you must understand that for the one that follows without a job, you will need to either:
3.1 go out of HK on regular basis to renew your visa and as such run a risk at sme point not to be renewed.
3.2 Look for a job of course and finally get sponsored for a visa (looking for a job while on a tourist visa is a very debated topic on this website: bottom line is most ppl do without any issue)
3.3 Create a company and get an investement visa
3.4 Get married
3.5 there are probably other options but I am no immigration officer...
4. Your list above is fairly straighforward: ie you can get a place pretty much anywhere on HK island (except the high end luxury areas that are the South and the Peak). But Sheung Wan, Sai Ying Pun, Wan Chai, Casueway Bay, Tin Hau, North Point, Quarry Bay are all within 25mn to Central and all on an MTR line (except Sai Ying Pun which is just close to Sheung Wan)
5. the trick issue will be "fully furnished" - not that common here
6. DO NOT in any case get a place without visiting first. You should come the first month on a Serviced Appartment and during that month look for a place.
7. Lantau is quite a trekk to Central (at least no way you get to Central in 25mn MAX -> ie the closest would be DB but that is 25 mn and some walking/bus on both side).