Hello Rainy and welcome to the forum

I live just north of Montreal so maybe I can give you some tips..
The first thing you need to do is get the water flowing away from the house...
I would order some top soil to make the ground around the house higher the the rest of the yard..
Then I would purchase some sod if you wish to have grass and lay it on the new soil..no plowing or digging invloved..
As far as plants,there are many options.It depends on full sun,half sun,how much shade etc...
Your zone should be 5 so just go to a garden center and ask questions...
It also depends on how much you wish to spend...
Good luck and I'd make keeping the water away from the house my first goal...
Diggy

How steep is the slope towards the house? Is the water problem made worse by where downspouts from the eavestroughs discharge the water? If so, consider what options are available to deal with that (e.g. can that water be directed through pipes to a roadside ditch...?) If regrading the slope towards the house would mean adding a lot of soil near the house walls, you may need to build a swale farther way from the house and shape it to direct the water past the house to a street drain if possible. You need to think about/analyze carefully what the sources of the water problem, and corrective alternatives, are so you don't inadvertently make the situation worse or spend money on a solution that turns out not to be effective.

all are pointing towards redirecting water away from the house and this is correct. You will have to examine how the water is coming down. You could use a weeping tile system to catch the rainwater and drain it away from your house and into a drain or you could use a dry river stone bed system to channel water down the slope and away from the house. The second option can be the same as woodyoak's recomendation. The idea is to catch the water far from the house as possible.

In my backyard, I employed the weeping tile system. My yard was catch all for all the rainwater coming from my neighbors' yards. It become a pond and boggy mess during rainy weather. So we had a trench dug and in it we laid down some gravel and on this a perforated type pipe with a sleeve (to filter out soil) and then covered/filled this trench with river pebble stones. The water as it came down was safely drained into this pipe/trench which then was led out into the drain located on my neighbor's side. I've not had any problems with the water ever since.

a dry river stone bed, is simply employing a swale and pebbles to lead water in the direction you need it to go. You firt dig out a channel, add some sturdy landscaper's cloth, top with various sized stones and pebbles. You can plant each side of the channel with plants that like to get wet (check out rain garden plants). It will look like you have a nice water feature.