Hi There I'm doing the same at the moment. Websites I'm using that are helpful to me are: viewit.ca (which has worked for me in other cities in the past), 4rent.ca & walkscore.com, (which is probably the most helpful one I've found so far for Toronto).
Also, to get to know the different neighbourhoods you could peruse BlogTO.
You could also find a realtor to help you find a home. They can forward you listings by email, or tailor viewings according to your needs. They don't always help people find rentals & have more access to condos, which may be something you'd like to consider as they often have perks rentals may not have. Often the realtor can argue a condo price down a bit, but this cuts into their share of the cut. Their cut is basically where the realtor makes an agreement with the land management to find a quality "renter" or "settler" for a unit in exchange for a cut of the monthly cost of the unit, this is taken from your initial deposit for the unit after the deal is made between you & the land management. Land management then gives the agreed upon percentage of the cut to the realtor. Your first payment to secure residency is first & last month's payments & any monthly condo costs.
Condo costs are in addition to the monthly "rent" & are maintenance fees to upkeep your unit as well as the building. One benefit of condo living is that you own the unit & therefore, can acquire equity, if you are interested in owning a house one day. Also, you could rent it yourself to someone if you happen to be out of country for awhile.
If you want to save yourself some of the work of looking a realtor can be helpful, but I stay away from Realtors myself, since I usually find listings online that are more in my price range & what I'm looking for. Also, I cannot afford condo living, or I would probably get a Realtors help. Condos are not always really expensive, they can be very reasonably priced sometimes, but I still do not make enough for this expense myself.
Many rental places may want an idea of your income, like proof of paystub & perhaps a reference from a previous landlord. This is fairly standard.
Also only when the agreement has been signed do you submit a cancelled cheque to secure your monthly withdrawals from the management. I choose to pay each month instead of automatic payments, but it may depend on the management of they will let you do this. In a large apartment building they may require automatuc payment. In a small one it is more personal & I prefer that. I like to have a good relationship with my landlord, so I take them my pay in person each month.
Anyway, best of luck to you!