Yeah, your front speakers sound like crap because you are trying to play bass through them and they are distorting. Eliminate the bass playing through them and they will be able to play mids and highs much better.
The sub can go anywhere. Bass is non-directional. Just throw it in the cargo area, but strap it down somehow, things move around a lot under hard braking/cornering.
You mentioned wanting bass, and you just won't get any appreciable bass from door speakers. And your mids and highs will greatly improve if you don't run bass to the door speakers.
I'm trying to give you the best bang for your buck.
You will get way way waaay better mids and highs if you replace the door speakers, but you will still not get any decent bass with them. You need subs for bass.
A powered sub is a nice all in one solution for bass. It consists of a subwoofer, enclosure and amplifier all in one unit.
Here is a darn good one that is pretty cheap
http://www.ebay.com/itm/New-Pyle-PLT...ht_3425wt_1165
Some people will say the "pyle" brand are junk, but I assure you they work well. It's just not a super name brand like alpine.
If you only want better mids and highs, get door speakers, but you will still have no bass.
Adding a sub and turning down the bass to the door speakers will give you bass and better mids and highs.
If you can swing it, get door speakers and a sub!
Adding rear speakers will not help your mids and highs. Mids and highs are very directional, and unless you can see the speaker from where you sit you will not hear it well. Most of the sound from rear speakers is absorbed or reflected off the rear seat.