There are many ways you can go, you asked a lot of questions but it sound to me like it boils down to
" I want a decent 4 speaker system by spending is whatever is required to make that happen without burning money needlessly".
If that sums it up, I suggest start with a decent USB sound card that has optical out. I bought one of these off the classifieds in my area for $50, used once for a wedding
Then, if you are positive you will never add a sub to the car, buy a decent 4 channel amp. If a sub might be in the plans later, buy a 5 channel.
Hook up what you have bought, tune it and listen. If you are happy....Done.
If not, next replace the front speakers with a decent set of coaxials or components, it's best to listen to them in a sound board at a store before you buy them, they all sound different and "good sounding" speakers is subjective.
Install what you have bought, tune it and listen. If you are happy...Done.
If not, then you may want to consider a sub and or processor depending on what you deem is "wrong" with the sound. But by getting a sound card with optical out and a 5 channel amp, you will not have to rip anything back out and replace, just keep adding until you are happy.