"My opinion is that you will get better sound quality by adding a amp to your front speakers then changing out the speakers themselves"
Per your above statement, I guess we agree that just replacing the front and rear with aftermarket speakers without amplifier and without Sub woofer will not make much of a difference.
Because I originally wanted just to replace the speakers and get it done, but due to the information I was given I went for a mono amp and a sub and kept the stock speakers.While my sound quality has definitely improved than what I used to have, I hope this was not a totally wrong decision.
The return period of mono amp is over, so I guess I have to buy another 4 channel amp if I need to power just the front speakers and get the installation done again(double work and double cost).
In the end, it is up to you on how much money you want to spend.
Best Buy has a total tec package that the total cost of labor would be $199.99 (for one year). I am sure if you say you are not happy with your sound or that it is lacking what you want that you can get a refund for your labor but then pay the $199.99 and do what you want. I also think you may be able to switch out the mono amp with a 4 channel amp. But there is a lot of things to consider. I think they are suppose to bridge two channels for the sub and power the front speakers with the amp and I think you will need the LCQ-1. I have two amps and the lcq-1 all screwed into the back of the rear seats and my crossovers for my front speakers are under the front seats (that is not normal...but my crossovers are SO BIG). Bottom line, if you are cash tight you can do the system in pieces since the total tec package is good for one year.
What 10" sub do you have? What is the RMS of the sub? I am going to presume you are not bass crazy (since you got a 10" and not a 12" sub).
I am also going to assume that a 4 channel kicker amp that is supposedly 360 Watt RMS (that is the one that I have $199) would be able to push your sub and front speakers. Personally I would also change out the front speakers with something decent and buy the LCQ-1 (this is needed in my opinion if you want to amplify the front speakers and it will drastically improve the sound quality).
Bestbuy doesn't sell anything good regarding quality. If you wanted to change out the front speakers I would recommend going to AMazon or somthing and buying something like the Alpine type R 6.5" speakers. You definitely want speakers that have a crossover and separate tweeters. Having after market speakers will improve the sound quality when amplified.
Bottom line.... if you go to BestBuy, (purchase the LCQ-1 ($225)... best buy does not sell it yet) and switch out the mono amp for a four channel amp. I am sure you will be much happier!!!! And if you are able to get the total tec package... you can switch out the front speakers at a later date (yyou have one year to do this). I was told that if I really wanted to switch out my rear speakers I can do this at a later date and the labor would be free but there is no need (rear speakers are just fill IMHO and should be amplified by the Mazda radio), what you want is a nice front sound stage.
Also do you have sub control knob? some kind of knob that controls your sub woofer? The LCQ-1 sells a knob called ARC-2 that works AMAZING. The LCQ-1 is a 6-channel line output converter plus 11-band equalization and bass restoration. If you get the LCQ-1 make sure they DO NOT USE THE "GTO" (signal-sensing turn on) so they need to use the 12-volt turn-on. Mazda's radio does not work well with GTO, basically using the 12 Volt turn on means that it turns on when you start the car.
The best buy installed 6.5" speakers in the door, 4" speakers on the top corners of the car and tweaters (this is my speaker set up). The top corners are designed for 3.5" speakers and they had to shave the car a little to get my 4" speakers to work. (you can't tell once the dash is put back on. These speakers retailed for $1,300.00 17 years ago and I purchased them from a store going on bankrupt for $189.00 and they have been in my closet for 17 years... lol.
Bottom line... price of labor $200.00, price of 4 channel amp $200.00, price of LCQ-1 $225 (on sale somewhere), price of wiring ect... $250, price of front speakers $200.00 (probably cheaper), price of sub ($150?). So cost for a decent system does add up but if you keep your car for a long time it is worth it IMHO. I also spend $400 and got apple car play/android auto from Mazda.
Personally I would have purchased the sub and 4 channel amp "used" and gotten the JL 300.4 amp and a JL 10" W3 or W1 or even W0 and purchased the front speakers new and the LCQ-1 new. I had the JL 300.4 but it broke due to water damage and was also 17 years old (but JL makes some of the best stuff around and if working would be MUCH MUCH Better then the kicker amp), the LCQ-1 fills the gap between a super good quality amp and what best buy sells (kicker amp) so even though I don't have such a good quality 4 channel amp the LCQ-1 makes up for it with it's 11 channel eq), I honestly don't know if having the JL300.4 would change my sound. I have a 12" W3 sub, being pushed with a 17 year old Apline AMp... but sub amps don't have to be good quality they just have to have the power to push the sub. Bass is muddy sound to begin with, a 10" sub would be cleaner bass than a 12" sub but it is all relative to how much bass you want.
I don't know if you noticed but I LOVE the LCQ-1 (the the sub knob ARC-2)... it makes SUCH a HUGE difference with the sound quality!!! And I was told I had no choice (there are other products but the LCQ-1 is the best IMHO and they are all about the same price +-$50.00) if I can't change out the head unit.
I am sorry that my post is so scattered. ANd I wanted to add to my first post that the front speakers are 6.5" from Mazda... I know this cause they gave them to me when I had mine replaced.