rainyevening,
Some of the fastest growing trees tend to get large. So you may want to keep them fairly far apart (10 meters?). You don't need may large trees to fill a yard. Plan for mature size, or you may be removing them later. Maples tend to have shallow roots and consume all the moisture, which prevents anything from growing under them. Not good if you want a shade garden.

I have had several water problems. Putting in some drain tile (buried hose 10 to 15 cm in diameter, not sure of the standard metric sizes) along that edge of the house and having it drain off farther down hill may help. If your house has gutters with downspouts, getting that water away from the house may help. Moving much dirt may take a backhoe (pay someone to do it). I had at least 3 different backhoes in my yard, 15 years ago for various water related reasons.

Plants are rated by hardiness zones, based on minimum winter temperatures for your area. You may be in zone 5. Conifers are great. You probably want winter sun to be able to warm the house a little to cut heating costs. So I may suggest to put deciduous trees (no leaves in winter) on the south side of the house.

There are some deciduous Conifers. Dawn Redwood is one, and mine is fast growing (over 1 meter a year). It is still a young tree, maybe 5 meters tall. It will get to be a large tree. I like ginkgo trees as well, and they seem to have few problems. Do not rule out smaller understory trees, that grow under the "protection" of a larger tree. I have put wire cages around my trees to prevent small woodland critters from eating off the bark and killing the trees. I plan to remove them after 5 years or so.

There is a lot to think about. I wish you luck and gardening fun!

The best way to deal with the drainage issues is to get a professional to survey and figure out the best way to site the new drains.....The people before had apparently done that before we moved in...we only have one "boggy" area now which is beyond the reach of the french drain down the fenceline....not an issue though - that's where I put my boggy shade plants (like astilbe).

15mx15m is quite large compared to most urban yards. Start with the trees....

As for trees - you need to decide what you want (like clay dirt says) do you want something that shields the house in the summer and drops leaves in the winter, do you mind berries dropping or nuts? Do you want a fruit tree? Do you want to retain a sunny part of the garden? Based on what you've said so far, a nice Musclewood tree might be a good option - It's a small native variety, grows to 20ft tall with beautiful leaves, interesting bark and produces nutlets that last into winter (so it looks like it's got Christmas ornaments).

Once you've decided on a tree or two - start looking at your shrub options (take into account again the same for trees, plus the habits and size requirements and the water drainoff requirements). Chokecherries, Juneberries, Spirea, etc. would all be good options, depending on your tastes and requirements.

Then you can go to the perennials and then the annuals and ground covers......