Welcome to the Fold Supercycle. It's funny to see that username since that's the old brandname used by Crappy Tire. Is there a link there?

Get your self down and join MEC if you haven't already. Then buy some Ritchey Tom Slicks and a few of the tubes you need and mount dem puppies up on your ride. Get a floor pump at the same time. It's the only way to fly when this is your only transpo. Fenders are there as well as racks, panniers and all the rest of the stuff. No point in worrying about lights just yet unless you plan on being out late. A seat bag is also a great way to hold your spare tube and tire levers as well as a folding allen set. And they've got a lot of other nice stuff as well.

For the rain I also suggest the most highly breathable stuff you can find. Sadly the best option I've used isn't sold there any more. It's lycra pants with a nylon shell "windproof" front. The lycra keeps me nicely warm in the coolest weather we get here while the nylon front sheds the rain and cold from the wind chill. Some water repellant spray works wonders at making the front water resistant for a couple of years and then I repeat the application. Similarly for the jacket. I used the micropore wind proof jacket rather than the serious rain jacket just so it would breathe better. Again it proved itself to be highly water resistant for the first couple of years and since then I spray it with water repellant every second year. Both the jacket and pants have got a good 10 years on them now and there's still a lot of life in them.

The velcro up the rear rain booties made from the nylon work EXCELLENT! But then I use clipless pedals. With platform pedals you may wear out the bottom straps sooner.

And no, I'm not a shill for MEC. It's just that they sell stuff that works so I buy it and find myself getting all enthusiastic.

Plan on the bus and skytrain for the two or three weeks of ice we get. Our ice is so close to the freezing point that it's hard but also slippery. It's not something to ride on. The good news is that if you are in an area where you ride on the normal roads rather than paths or side streets the main routes clear very fast. You may only need to bus or S'train for 6 to 12 days in total.