It looks like you have mostly dandelions...you can use a broad leaf herbicide like 2, 4-D (i.e.Killex) if you don't want to dig them all out by hand. I don't have a big problem with weeds so can manage with the hand held weeder, but I can understand if you require something "quicker acting". There will be a few folks posting here that will tell you to eat them instead.

And mow at least once a week which will favor the grass and somewhat damage the dandelions. Depending upon the kind of grass, cut at 2.5 or 3 inches tall.

Where in the world are you?

What kind of grass is growing there?

What is the soils pH?

How much organic matter is in that soil?

What is the level of nutrients in that soil?

A good healthy soil will help grow a strong and healthy turf that could crowd out the "weeds" without spraying poisons.

kimmq is kimmsr

Looks like one of the plants called dandelion, not creeping Charlie (Glechoma hederacea.) Probably a Lactuca or Sonchus. If you're able to add some more close-up pics, someone should be able to help you with a more specific ID.

Growing a perfect monoculture of 1 kind of grass is not a requirement for owning a home or being a good person. If these non-grass plants are soft & not unpleasant to walk on/around, I wouldn't worry about them. If it's a significantly shady spot most of the day, grass might not grow well.

If you choose to use a product, the label should tell you which plants it does or does not harm, and how and when to use it effectively. You may want to try to ID your grass also, so you'll be able to compare it to the info on the product labels.