The water shows you were the low spots are. Measuring how deep they are will tell you if you need to do anything or not.
For a concrete finish, I don't know if self leveling compound will work. It's always quite a bit darker when I use it, and I've never seen what it looks like over a period of time. It dries so quickly that you can tile over it the next day.
I don't have any experience with staining concrete other then talking to the guys after it's done. Prep and the condition of the slab are important, but from what I understand, they will stain anything. There is ideal, and then there is what they have to work with. If you put a clear coat on it to make it shiny, you will see more imprefections then if you leave it dull.
I personally don't care for concrete floors. I tried them, and some of my clients have them. In my opinion, it's a fad that is popular right now, but like allot of things that people feel they must have in a house, it goes out of fashion after awhile. I've tiled over most of my concrete and plan to cover the rest with wood next year. Some things are timeless, others are gambles on how long they will look good, or something that you want.
Eddie