Since your biggest investment is your house, check your foundation, basement, garage, and any cement pads; are there any issues with cracking cement? Is the water affecting any part of the soil under your house, where it's always damp? That's the runoff or ponding that may not really show. Are pipes under the house shifting (laundry, blackwater, gas pipes) causing slow exit from the house? Is anything backing up inside? If there's any sign of shifting, then uphill from that
should have some water diversion. If it's ground water that you can't really see, then you should consult an engineer who can create a plan with
underground pipes that divert the water.
If it's just runoff during a heavy downpour there are runoff creeks that can be established that are "fake creeks," a snaking, garden design kind of gully lined with cobble stones and few big boulders for interest. That can go off the property, but not onto your neighbors' property, or you might cause them water issues, and then there's real trouble.
Since you've lived there a while, there must be footpaths you use most of the time. Those can be a foundational starting point, because they indicate how you prefer to get where you're going. They probably avoid whatever muddy situation is created by the runoff and are in good locations. Those footpaths are nice to have them wide
enough so two people can walk
side by side, so 4 feet. That is also helpful if you put a wheelbarrow or tools on the footpath, you can still get around them without stepping on plants. Yards around houses can have a bigger scale of design than just a cow path width.
Then consider the style of garden you want, peaceful Japanese with lots of rock, or English with lots of flowers, or
native plantings, or modern with stone walls, formal with cement, casual with brick pathways and walls, vegetables with flowers, etc. That's easy to research on the internet, find something that makes you say, "Ahhhhhh," and that you keep wanting to find in pictures. Try not to make everything fit in tightly, so you have room to move when working on plants, it saves your back, gives you room to take tools and glove/clipper containers with you.
Do you really want all those trees, or is one enough? There might be more issues with shade and mold, especially on the roof or around windows or the foundation on damp soil.
Since you've got a southern exposure, there is the possibility for passive
solar heat and more light into your house if the trees are not there, unless that's too hot in the summer. But if mold and droppings from the trees seem like an issue, maybe just one tree for summer shade might work just as well out front, and open up some area for planting.
If you don't really want to garden, then
perennial landscape is easy enough, shade plants in front under the big trees like rhododendrons, azaleas, hostas, then add something more structural for interest, like a terraced hillside, a sitting area with a bench made with rock or stone pavers, whatever is appealing.
It's really helpful to draw out a bird's-eye view plan. Draw it in as many ways as you can think of, have a plan. Use colored pencils, and graph paper with real sizes. I used to like to work off the cuff, spontaneously doing one section at a time, but I usually ended up having to redo it. A lot of ideas, practical and creative, will come to mind when there are fewer distractions at the table, than out in the garden, in my
experience.