Audio Questions, Possible Upgrade

I am a complete noob when it comes to car audio, it's a science I never cared much for and so here I am with a toast factory amp and a new Alpine head unit with no idea and no experience. I have the 10-speaker E36 set up on a 95 BMW 318ti.

I picked up a nice 4 channel Sony Xplode amp to replace the factory one, though I received a puzzled look from my mechanic telling me I'd need crossovers for all the speakers as the amp is a wide range amp (or something) and doesn't support lows/mids/highs separately. He then told me there was no point doing that since the factory speakers are garbage, which I fully agree with.

So I have no idea where to go from here. Should I just replace the mids/lows with 6 all-range speakers and just forget the tweeters? Keep in mind I am not a car audio fanatic and don't need to invest in subs or a crazy expensive set up right now. I just want something affordable, but still a good listening experience.

Any ideas, links to write ups, etc would be appreciated. Also feel free to also explain what my mechanic was talking about, what possible options I can explore and how the stock wiring will come into play.

Thanks!!

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