My dad swears by the book, "Lawn Care for Dummies." You might want to get a copy of that or some similar book. My caveat would be, and I'm not 100% sure, but it is my educated guess, that the tree in your front yard is a Norway maple. They are notorious for excluding and impeding the growth of anything in their vicinity. Their roots are so aggressive that they suck away all the nutrients and water so that anything that tries to grow under them just can't compete. Add more water and nutrients or soil under them and they will just suck away more! Plus the dense shade will limit your choice of plants for by your foundation.

Edited to add that it could be a silver maple, but again, can't tell from the photo. Many of the caveats still apply for that tree as well, notoriously "rooty."

Still lots of options but chose ones that can tolerate shade. Your two choices are just accept a sparse lawn (it could probably get somewhat better but with that Norway maple it will never be lush) or cut down the tree. But first show a photo of the tree's leaves and close up of the trunk and branches to confirm my suspicions. If it were me, I'd do the best I could, not try to have the perfect lawn around that tree, put edging on the beds around the perimeter like you mentioned, and add some good black dirt and replant with some nicer things in those areas. Bear in mind that shade tolerance is a must for your yard. You could mulch or put a little patio or gazebo out there somewhere if you wanted a play area with less stuff on the ground for bugs to hide in. But outside = bugs pretty much.

Do not mulch under your tree. It won't do any good. The trees will just send out more roots to grow on top of the mulch. Most trees can do with an inch or two of mulch but no more. Those volcanoes of mulch under trees just kill them slowly by suffocation. In fact, keep mulch away from the trunks of trees. In the case of Norway maple, just try and overmulch them, they will just respond with, "Bring It!"

There are many schools of thought on seeding a lawn. If you have more money than time, I just used to shoot out seed with my spreader before I knew there was going to be a big rain event. Some grass sprouted. Over time, it filled in. My strategy was a "survival of the fittest" strategy but it worked as well as any other strategy and was a whole lot less work than all the patching and watering I did before. Sometimes I would just sprinkle seed on bare areas. I use occasional weed killer applications and hand weeding to keep down the weeds. That's how I got my lawn into shape, a combination of weeding and reseeding over time. You'll need to do both. Grass seed has certain temperature conditions for seeding so check the package and don't seed until you're well into that zone. But then grass stops growing when it gets too hot also, so seed in spring and fall. Your biggest challenge is going to be the tree, so like I said, lower your expectations.

Landscaping is a combination of using outdoor elements to "decorate"/enhance the house and create a setting for it. Based on your pictures I wouldn't have any idea what to tell you, as we only see parts of your house from the "ankles" down. There is no way to get a sense of what it and the surroundings look like. I order to rectify that, stand about even with the tree but in line with the front door. Stay in that spot for all pictures, merely panning the camera. Begin by aiming the camera to the far left so we can see your neighbor's property and take slightly overlapping pictures while you pan the camera to the right. You're finished when we can see the neighbor on the other side. Hold the camera in the vertical format so we can see more of the house. Also, while standing in line with the front door, back up, possibly into the street and take a picture that shows the whole front yard from corner to corner and the trees in their entirety.

I pinkmountain, thanks for the advice. I'll be sure to look into the book you referenced. Attached are the pictures you requested of the tree.

We considered cutting both trees down actually. Should we be concerned that it's leaning towards the street?

Yardvaark, I will be sure to post the full picture of the yard tomorrow.

Well, now it looks like a red maple to me. It is probably "leaning" towards where the sun comes from. If it looks healthy, then I wouldn't be concerned. But you have to step back away from your home to take photos in any case, can't tell much about a tree just from a window into part of the trunk. Same with the other issues in your yard. Healthy lawn depends on a lot of big-scale factors like sun, water drainage, topography, direction, other houses nearby, etc. Also, if you want to highlight certain features of your house, we have to see the whole house.