There are at least a dozen people who have done audio mods and the trouble is we can't listen to the cars side by side, but if you trust everyone's impressions at face value, depending on how picky you are about car audio I think one can make reasonable choices, realizing that the head unit equalizes the signal even with all EQ settings off, all DSP off - it's strongly coloring the signal, especially in the bass region.
If the shop tests the head unit output with a frequency sweep (via bluetooth or AUX input) and measure the frequency response at the speaker terminals then they may see huge bass swings, peaking at 60 hz and a dip at 120hz - I have not done this but someone else did and that's what they found, so it's not just a matter of the speaker's frequency response, cabin resonance, etc. This to me is the biggest weakness of the system - it's forcing an artificial sounding bass.
So if all you want to do is change speakers and not touch the electronics, I would seek out door speakers that tend to be strong at 120hz and weak at 60hz, while still having decent mids, and put in whatever reasonable quality tweeters you want. Then if you want low bass you'll need a subwoofer for 40hz or so.
If you get the Rockford Fosgate amp I'm not sure how the low frequencies are EQ's but it's not the same as directly from the head unit and probably much better, but it doesn't address the lacking tweeters.
If the audio shop is willing to test the system's frequency response I would like to get a graph of their findings - only one person did it so far and I'm basing the above on that person's test results plus my own listening impressions before and after changing speakers.