I'm an international student in Vancouver. My wife and I moved up here in May of this year from the U.S. I don't know where you're coming from, but ift its the US, a couple of things about rentals/housing in general you should be aware of.
1. Generally speaking, you're going to find that housing/apartment/condo sizes are noticeably smaller here than in the US (square footage-wise).
2. Finding someplace that will accept pets of any kind, and dogs in particular, is going to be extremely problematic. The local want ads and leetr-to-the-editor sections of local papers are FULL of local residents desparate to find places that will accept pets!
3. Likewise, if you smoke, you're also going to have a tough time finding a place.
4. As a point of reference, My wife and I rent a condo in Yaletown roughly 950 sq.ft., 2br, 2ba, 1 parking space in underground garage. Our rent is $2700/month. We have 2 vehicles, so we rent an another garage space from the Strata for an additional $135/month. Water/sewage/trash pickup/heat (baseboard stem radiators)/gas (fireplace) are included in the rent, hydro and cable are extra.
5. We found our place via Craigs List. A great resource for housing info are the MANY local free newpapers, some daily and others weekly or bi-weekly. Every area/subdivision seem to have their own newspaper here, not just municipalities. For example, Burnaby, North Shore (N. and W. Van), False Creek (Van), Coal Harbor (Van), Joyce-Collingwood (Van), etc. all have their own local rags which contain info about and ads for housing and rentals. A GREAT one-stop place to get a bunch of different ones all in one place is inside the public market at Granville Island.
6. In addition to condos/apartmentsin low/mid/high-rise buildings, MANY homeowners here have houses with a second suite that they rent out. Usually the owner lives on one floor and the other floor is rented out. These alsmost aleways have separate entrances, separate meters for utilities, etc. You'll see these listed as upper or lower (or basement) suites. Unfortunately, they raerly include a dedicated parking spot, so street parking is all you'd get. As anyone up here can tell you, street parking is EXTREMELY limited (particularly free street parking), and usually comes with RESTRICTIONS, such as NO PARKING PERMITTED from 6:00AM to 9:00AM and from 3:00pm to 6:00pm on weekdays on many streets (rush hour). But rent can be somewhat lower and roomier.
7. Public transit is excellent so seriouslyt consider more outlying areas such as Richmond to the south, Burnaby/Coquilam/New West/Surrey to the east. No point in heading north or west as all you find is mountains or ocean!
Best of luck and welcome to BC!
Ingo