If you have the invasive honeysuckle variety then you need to get rid of it. There are other less invasive shrubs you can use to replace them. Don't plant Nandina as a replacement, the berries are toxic.
Viburnums are a better alternative.
Other than cleaning up weedy and messy areas, try to live with it for a year to see what is already growing there. My first year here I found so many wildflowers and naturalized bulbs. There was a dogwood in the wooded area that I moved to a sunnier spot and a very nice strawberry patch.
Check where the sunny areas are so you can plan where to put a garden if you want one. In the meantime you can plant in pots and tubs. Spend your time plotting out zones for different activities. Although I would set up a compost area right away so you'll have someplace to put your leaves and other yard debris.
Watch for low areas/flood zones. Also make sure you know where the actual property lines are. You don't want to get in a property line dispute years down the road.
Is that low lying green strip a drainage ditch? If so I would plant some wetland plants along each side, leaving a place in the middle for a path or bridge going over the ditch. I would probably put in some sort of water feature like a pond or fountain on the far side right of the ditch.
I can see a shade garden full of naturalized bulbs and, as the season progresses, lovely tall hostas and ferns. That is the back half on the right. Then in front of that, close to the house, there would be a mulched area with a table and chairs to set in the yard and watch fireflies and relax in the evenings. On the left would be some sort of trellis/screening with flowers growing with the woodpile and compost pile in front of that. Then going toward the house on the left I would put in some flowering shrubs with flower beds in front of that.
But to give good suggestions I would have to know what you want from the area and what kind of plantings you like. Do you like spending time outdoors? Do you want to attract wildlife? What kinds of wildlife do you like? Are there any animals (like spiders, snakes, etc) that you definitely don't like? Do you want to have a large, provide most of your own food garden? Would you prefer wooded, shrubby areas or do like open mowed areas? Do you plan to make a concrete or brick patio in the future?
I know what I would do with it but that might not be what you want to do there.