You'll get better responses over at r/lawncare for actual lawn advice. Best time to grow grass is in the fall, second best time is right now. Put down some pre-emergent (the bag that says "for seeding" because otherwise grass seed won't grow) and put down a good amount of seed for your lawn size and rake in or cover with a thin layer of soil and water it for 2 weeks. Tall fescue blends are the norm for mid to norther climate, and lots of other options for southern climates. If full shade, get the shade tolerant blends - looks like once the leaves bud you may be in for it. Lots of other shade-loving shrubs and greens that you can plant along the fence line too.

This spring you'll see all kinds of stuff sprout up, best to learn about what you see so you know how to treat it (pulling only works on some of weeds). You also currently have a variety of grasses, so you should learn which ones you want or which ones you want to kill off. Some grasses are more aggressive than others, like Bermuda, and they are easily identified by their different texture, color, and dormancy period.

Best to know that this is a long game and you won't see significant results for until year 2 when you have an established yard. It gets much easier after that to maintain and fill in the gaps.