Like in other cities, the principal issues will be cost and location. With respect to location, the major issues will be crime rate, the proximity to public transit, commute times (if relevant) and proximity to amenities that you will regularly use.
Vancouver, as Canadian cities go, is among the warmest. Heating will not be as huge an issue as it will be in most of the rest of Canada. Electric heating is more common in areas in less intense winter cold, but is the most expensive heating source. Natural gas heating is much more common in the colder regions, and has much lower costs. In Vancouver and suburbs you are likely to find both.
Many landlords are now doing credit checks. If you are new to Canada, you will not have a Canadian credit rating, so do not be surprised if you get questions about your situation as a result.
Look online to get reviews of landlords. There are some very large landlords in most Canadian cities, that own significant stocks of apartments. Some of these landlords are good; some are bad.
A written lease is a must (even though, by default, a standard lease applies). Oral leases are hard to enforce - who knows what was said?