Actually, I will answer in reverse first - what you should not bring.
What you should not bring are:
1. Anything that are consumable and can be replaceable easily (such as shampoo). If needed, travel size only.
2. Anything that are cheaper in Canada or the U.S. (such as notebook)
3. Any original document unless it is necessary (such as HKID)
What you should bring and need:
1. Anything that you need that you can't buy in Canada (for example, medication, lotions)
2. Any document (in copy) about your background (like immunization record, medical history)
3. A U.S. B1/B2 Travel Visa.
In order to understand this list, you must understand the location you are going.
Burnaby, BC is within the Greater Vancouver area. Due to high numbers of immigration from Hong Kong, a lot of products in Hong Kong in fact are also available in Vancouver, although it may be more expensive. So there is no need to move the entire Hong Kong to Vancouver.
Also, due to the close distance to the State of Washington, U.S., a lot of Canadians cross the border and buy their household goods from the U.S. Eventually, your classmates will get you to the U.S. and do shopping. That's why you need a U.S. visa.
Last but not the least - the clothing in Hong Kong does not fit Vancouve's weather. So you simply have to bring what's enough for the winner (except underwear). You will have to buy everything after you arrive.