ok here's what you want
Music tastes aside: please realize you either need to buy a Metra dash kit (which I JUST bought and is EASY to install but QUITE pricey at $170) or you need to buy a line output converter (or hope your factory head unit has preouts from it which I doubt it does). You are looking at either buying the kit and a head unit or buying a preout converter. Either way you will get a better sound out of adding aftermarket speakers that's for sure, same with upgrading your head unit to existing speakers in your car.
I spent $580 on a head unit, a 4 channel Hi-Fonics amp, a pair of 6"x8"s and a 6.5" component set. Realize if you are only worried about yourself you can go with a head unit and a set of components. I, however, wouldn't recommend running comps off of a head unit. I suggest amping them. At least a nice 2 channel amp thatn you can find for about $150 or so. Remember you get what you pay for.
As an update I popped a set of dual voice coil 8" subs in my doors (with some work) and ran those off of channel 1/2 of my amp (getting almost 175 watts apiece) and then I ran my comp set and my 6"x8"s off the 3/4 channel of my amp and it sounds SUPER good. I threw a sheet of dynamat behind each speaker to help with the road noise and the resonance. Keep in mind you have to PAY for better sound no matter what.
This is a temporary setup for now but I plan on adding an upgraded alternator and a few batteries. Adding a 12" sub and a 3k watt amp as well. Using a ported box tuned to 35 hz for that nice kick drum. Just because it booms doesn't mean you have to listen to rap. I can't stand rap (except old school hip hop) and in fact, I listen to metalcore mostly. Nothing feels like that kick drum and double bass in your chest. Don't think just because it sets off alarms it's rap. I had 6 10"s in my last car and it was LOUD and punchy but CLEAN and very obnoxious. Music is what drives some of us and you don't have to listen to rap in order to wake the neighbors. Just remember when you turn it up it's hard to keep the pedal from the floor, whether you listen to rap, rock, or metal.
A LOT of people I know like that kick in their chest. Personally when I'm blazing down the highway at 90 mph it's nice to know that even all the "dopest cats in my hood" are hearing me coming from 15 blocks away. And YES I do that with metalcore. People at work hear me coming a few blocks away 6 out of 7 days of the week. If you have questions message me. The Mazda 6 Metra kit is pretty in depth. Hope this helps you.