Sony Xplod subwoofers are a false economy: The sound quality is not very good by any means. I feel pretty confident that if you put a TRUE 2200 watt RMS amplifier on two sony Xplod subs you would have two things: way too much power for your needs and two broken subs. A great quality 600 watt amp would still be a bit much for those two subs, honestly. I would rather get one Alpine Type R than two sony xplod subwoofers any day. As far as amplifiers, quality is the first thing to look for like said before. If you want to save money, I'm a fan of used. I would rather buy good quality used items than new mediocre items.
For Dubstep with stock doorspeakers, it seems that audiophile quality isn't the utmost priority, you just want something in the low range that fills in what your stock speakers are missing.
You need several things: first, you don't want to tax the electrical system of your car by getting a monster amp and sub that would way overpower your factory door speakers. You need an efficient system.
A Class D amplifier is much more efficient than a class A amplifier, so basically look for a Mono (single channel) amplifier. You won't notice the difference at all. For an efficient sub, you can increase efficiency by either a higher sensitivity rating, larger box, and box type. A 15" sub is too muddy, 10's are great but a 12" woofer has about 45 percent more surface area.
So now you need: 12" subwoofer, mono amp. More affordable mono amps generally generate most power when encountering a 2 ohm load, so you either need a 2 ohm subwoofer or a subwoofer with dual 4 ohm voice coils. Dual voice coil won't make a difference in sound quality, it just gives different options for the matching up of amps to subwoofers. Price should be the same either way.
If you are running two quality subs, you'll need at least 4 gauge wire. This type of setup typically draws enough power that your headlights will dim each time the bass "hits," so I'd stick with one subwoofer, but maximize your volume capability by using a vented box. This should let you use 8 gauge wire, and this should be good for a 12 foot run with a 400 watt amp. That's pushing it a bit, but hopefully you won't be maxing out your amp and drawing so much current anyway. If you wan't two subs just because you're stuck on the idea of it, then run 4 gauge and a bigger amp but you'll need a capacitor to buffer your electrical system.
Some amplifiers have high level inputs so you can just run some speaker wire from the rear speakers to the amp to get the audio signal to the amp. If you get an amp with only low level inputs, then you can either run RCA's from a subwoofer output on your new head unit (I'm not a big fan of the low/mid level Sony's, though... Pioneer and Alpine or other higher quality) or you can get a high level input converter that converts the high level signal (rear speakers) to a RCA outlet.
I would want a head unit that had subwoofer level control; you might love all that bass with your dubstep, but when you go to listen to NPR or something the bass is overwhelming and annoying.
Another feather I would really want in a head unit would be a high pass filter for your door speakers. If they are fed a full range signal, then they will waste power trying to play frequencies which they are not capable of reproducing. A high pass filter will only let higher frequencies through that they can actually play, thus making overall sound quality better.
Recap:
Single channel Mono amplifier of reputable quality in the 350 - 400 watt range.
Single 2 ohm 12 inch subwoofer - you'll either need a single 2 ohm coil or dual 4 ohm voice coils. Either is fine.
Vented Single subwoofer box. Stuff some polyfill in the box to help with unwanted resonance as well as making the box think it's bigger.
8 gauge power/ground wire will do, 4 would be better
Head unit with sub rca outputs, sub level control, high pass filter
Alpine Type R is a great bang for the buck sub.
Used quality >> new mediocre