Hi Panos,
I live in Vancouver (for 3 years now) and so I can give you my opinion. Rupeshhari is right. You cannot apply for Permanent Residence while on a TRV (Visitor) within Canada. Also, unfortunately you cannot apply for a work permit from within Canada unless you fulfil one of the conditions listed on the CIC website (follow link below, choose the visitor self assessment tool which will direct you to the list of eligible people who can apply for a work permit from inside Canada):
http://www.cic.gc.ca/english/e-services/extend-visit.asp
If you fulfil one of the conditions above, you can apply to Vegreville, Alberta to change your condition from a visitor to worker atleast 30 days before expiry of your visitor’s visa. You will be required to satisfy all conditions for a work permit and in most cases will need a job offer and might also need a positive LMO from HRSDC. In my case, my partner came to Canada on a visitor’s visa and was able to change conditions and obtain an open work permit within 2 months only because I had a valid study permit.
Of course you can also apply to extend your stay as a visitor but a visitor's visa will limit you in so many things e.g. medical insurance. You cannot be granted the British Columbia Medical Services Plan if you are a visitor (medical expenses are very expensive unless you have insurance). As a visitor, you have to buy your own temporary insurance either in Canada or from your country.
All in all, it can be hectic (and most times impossible) getting things done on a visitor's visa. The best advice for you would be to be patient and enter Canada as a PR. However, as Commonwealth advised, come and visit, return to your home and decide.
You will like Vancouver. Very beautiful (mountains, ocean, fantastic weather - Vancouver is hosting this year's Olympics but we've had no snow so far!!!), great schools, parks, health care is good. It is multicultural so you will surely not fail to fit in. This however comes with a price tag - It is generally expensive living here and you must be prepared more so for family of three.
Essat, Vancouver
