Project: back yard

Here is a drawing of my yard from above:

As you can see, its pretty big, and has a nice fence for the doggies. However, it drives me nuts that the landscaping looks like someone started to terrace and take care of the left side, but stopped years ago. Chaos has taken over! I really want to make it look like someone cares about it. The grassy part of the yard is good for the most part, but the far right side by the fence gets really boggy. Since we have moved in, we put in the bed to the left of the porch, planted the daylilies outside the fence by the road, and planted the redbud tree. I really like the forsythia and the holly, but there are FAR too many trees in general. I love that we have established, mature trees, but 11 is a bit much! Especially because most of them are oaks which make the soil very acidic and the yard very shady. I want to take down some of them, but Brett and I disagree about which ones and how many.

So to make a long story short, I am in the midst of planning out my dream yard. Does anyone have any suggestions? I want to keep a good bit of the grass, and make the rest of the yard look cared for and planned. The grassy part tends to get too wet, so any suggestions about what would suck up a lot of water on that side of the yard would be great!