Disclaimer: I live in Missouri, where it doesn't snow as much as in Chicago.
For the snowblower: gas engine. In theory, you can get 2.4 horsepower from a standard 120 V outlet, but in practice it's less; it's easy to buy a gas engine that is stronger than that. Also, as @Marc M. noted, it's slightly more likely for the electricity to be out in the winter.
Try to get non-ethanol gas for the snowblower; small engines like it better. Also, try not to use old gas - until you know better how much you will use, buy something like a 1 or 2 gallon gas jug. You'll make a few extra trips to the gas station, but the equipment will run better with fresh gas. Also, sometimes smaller jugs make the fire marshal happier. If you find the gasoline in the jug is more than about two months old, dump it in your car's tank, then fill up the car (the rest of the way) and the jug at the gas station.
If you let the gas from February sit in the snowblower until December, or the gas from October sit in the lawnmower until next April, you're gonna have a bad time. You can either run the engine until it runs out of gas, or get Sta-bil (a gas additive) from the discount store or car parts store. Mix the Sta-bil with the gas and the gas will "keep" better.
I don't know any specific brand to recommend. You might go to the library and check Consumer Reports magazine for a recent snowblower review. (You can't see their ratings on their web site unless you pay.) Or, wait until it snows, and then go around to various commercial properties to see what brands the snow services are using. (This may be a little late for you, but you can figure out which one to buy *next* time!)
You should also get a good snow shovel (hardware store) and maybe a broom - there will be small areas, like steps, where it will be hard to use the snowblower.
For the lawn, if all your grass is within 100 feet of an outlet, and the lawns are relatively "open", you might consider a corded electric mower. Get a good 12-gauge, 100-foot cord to go with it. The nice things about an electric are that it always starts on the first try every time, and you don't have to store gas. The bad things are dragging the cord around, and that they usually aren't as wide or as powerful as a gas engine. Dragging the cord is why I said "open" - if you have a bunch of trees or swingsets or whatever to navigate, getting the cord to do the right thing gets trickier.
I don't like battery electric mowers; I feel the power requirements hit the batteries too hard and will require replacement batteries too often.
If you get a gas mower, again, use non-ethanol gas, as fresh as you can. Check the lawn services to see what brands of mower they use.
Usually you also want a string trimmer (weed whacker) for the lawn. Can be gas or electric, according to the same criteria for the mower.
I've done so little salt in Missouri that I just spread it by hand when I do use it.
I hope this helps!