And now for the advice, warning, this might get a bit windy. I try to fully explain, instead of being too pithy.
, looking at your pictures, there's a couple of different approaches you can take. I think the best thing is to find out in more detail what you're out to accomplish.
You've got all the old-buddy weeds that bedevil me at my place. I've got half an acre, so there's a bit of weeding.
I'm an attorney now, but I used to operate a garden shop and one of the things I did a lot of out in Moreno Valley was helping people start lawns, both sod and seed. And, I did a couple of my own from seed, one for me and another for a lady friend. ("If that's not love, what is?")
That fine-bladed grass in your pictures looks like Bermuda grass, which, properly used, is one of the toughest [expletive] grasses. It's tough as Marines and, well-treated, also just as invasive. It will be a nice green carpet, that grows right back from trampling feet, big dog traffic, etc. It also vigorously invades any area it hasn't already.
But BG has a couple of problems, too: (a) it won't grow well in the shade, at all; and (b) it turns brown in the winter for dormancy.
So, my first big question is: do you want to keep the Bermuda Marines of Doom Grass? Or do you want something else?
DON'T get bluegrass; it's much too fussy for here, too hot in summer, way way too much water. If you don't want BG I recommend tall fescue, or, for a spreading lawn in the shade, St. Augustine Grass.
This is going to take some time, but I promise it will be time well spent if you want a nice lawn.
Even if you want the Bermuda grass, you might be better off nuking with Roundup and starting all over.
Tell me your plans, and I'll do all I can to help effectuate them.