I am Immigrant.com

Those are the first things you need to buy after you rent an appartment:

1- A Mattress to sleep on
There are standard dimensions for Mattresses,
Twin : 39 x 76 inches ( 99.1 x 193 cm)
Twin X-Long : 39 x 80 inches (99.1 x 203.2 cm)
Full : 54 x 75 inches (137.2 x 190.5 cm)
Queen : 60 [...]

How to deal with your landlord:
Not all landlords are good people so you really need to know your rights and your duties.

These are models of notices that you can receive from your landlord and how to reply to them and the notices of the tenant, that you may need one day.
http://www.rdl.gouv.qc.ca/en/avis/avisproprio.asp

If you have a problem [...]

It will be very good if you plan to open an account first thing you come. It useful to open 2 accounts  one with US and one with CA. Even if u don’t put money.

RBC bank http://www.rbc.com is very famous and has many branches in Montreal.

Why?
The point is that this will be very useful to [...]

Well.. You  need to start searching for a place to stay in probably 2 months before you come.

Use these websites to rent an apartment and buy used furniture

http://montreal.kijiji.ca
http://montreal.en.craigslist.ca
http://www.lespac.com
http://www.canadarentals.net/city-view.cfm?CityID=1673
http://quebec.rent-index.com/
http://www.viviun.com

Most of the contract you will find are annual contracts so you will be committed to stay in it for a year.
Also it might be difficult to get [...]