I also wanted to add that I also have dandelions, clovers, and the unknown weeds pictured below on my lawn. Is there a single way to handle all of these?

The top photo looks like crab grass the bottom looks like one of the chickweeds and there is no one way to control all of the unwanted plants you list. Crab grass needs a grass killer while the others need a broad leafed "weed" killer.
What is the soils pH?
How much organic matter is in the soil?
What kind of life is in the soil?
You can spend a lot of money on stuff that poisons the environment but gives you a good looking, mostly "weed" free lawn, or correct any soil problems that exist and grow a good healthy lawn that is not necessarily "weed" free.