Why need rear speaker unless you sitting behind all the time and not at front at driver seat? If really need just get a pair of cheap speaker for the sake of it. Normally a pair of front speaker will be enough to fill the whole car and the rear seat will still hear the music.
This been said, you need the front to play loud to fill the car. Therefore an amp would be the best solution. As for what amp? then its budget time.. go to any friendly installer to see what they have.
Just imagine a concert hall or such.. All musician and singer are all at front.. so speaker in front will do... Don't confuse yourself with Cinema with speaker at the back.. those rear speaker are for effect and such... you not watching movie in the car.. if music just the front will do... in a concert hall they don't put speaker at the back right? for those sitting at the back/rear right?

Sorry for jumping in now .. about to dampen your mood... Seem like you gotten your amp and woofer.. do note some installer will not want to install things not sold thru them as they don't want to get into hassle of issue if the amp/woofer you bring have issue/problem. Some more you plan to get the rest of the stuff yourself (wires and such) and that will bring another set of issue as anything not sold thru them will be at your own risk and some installer not willing to proceed just labour alone and bear the equipment risk. Not to mention that they already lose profit from equipment sale and need to bear risk of equipment failure whether accidental or such.
As being expensive, depends on the installer.. some have high end equipment and their installation price reflect the equipment at their workshop. You see Sine Slope machine and such there but not all willing to invest in those...