I replaced everything in my 03 with the Mach system, and have done it many times for other people as well. The way that I do it makes it easy and requires no more work than if it were a non amplified basic system.
Run the amp power wire(s) from the battery (do not connect yet) into a fuseholder then through the firewall on the drivers side, then route the wire to the trunk, also down the drivers side.
Run 3 sets of RCA cables, 4 pairs of speaker wires and a remote turn on wire from the radio location down the passenger side to the trunk area. I always wrap these wires with electrical tape every 10" or so to keep them organized and in a nice bundle. Also, I mark each end of the front RCA with 1 line, rear RCA gets 2 lines, and 3 lines for the sub RCA, so when you are plugging them into the deck and amps you know what cable is what.
Connect the 4 pairs of speaker wires at the radio location to the 4 pairs of speaker wires on the aftermarket wire harness (Metra 70-1771) that plugs into the stock radio plug. These are the wires that would normally be connected to the deck output if you were not using a 4 channel amp.
Connect the remote turn on wire in the bundle at the radio location to the remote turn on lead on the new deck (Blue/white). Connect the 3 sets of RCA cables to the proper outputs on the new deck. At this point you can complete the deck install.
Next I remove the factory amps and enclosure from the rear deck, and install the new speakers. You MUST connect the new speakers to the factory wires that were connected to the factory tweeters. They will have a gray 2 pin plug with a clip on one side. (the wire closest to the clip is the negative) The rears can be found on top of the rear deck lid, and the fronts can be found just below the factory tweeter behind the door panel. If you are using a component set of speakers in the doors, you will need to find a location to mount the crossovers in/on the door, then extend the factory wires going to the stock tweeter and connect them to the input of the crossover. I always mount the crossover directly behind the armrest of the door panel as there is ample clearance for them.
Run a set of new speaker wires from the woofer output of the crossovers through a hole on the inner door skin and route them to the stock speaker location, making sure to keep them clear of any moving window parts. To properly mount a 5.25" or 6" midrange, I cut a 5 x 7 plate out of ABS plastic using the stock speaker as a template, then cut the proper size hole in the center for the new speaker. Mount the plate to the stock speaker location, connect the new wires to the new speaker and mount the speaker to the plate.
Next, run a new speaker wire from the tweeter output of the crossover up to the stock tweeter location. To mount the new tweeters in the stock location, I use a metal strap, called backstrap at stereo shops, and bend/cut it so it can be mounted to the stock tweeter pod using the factory screw holes that held the stock tweeter in place. Once the backstrap is bent into the proper shape to fit into the tweeter hole, mount the new tweeter to the backstrap using the supplied hardware that came with the new speakers, then mount the tweeter/backstrap assembly to the tweeter pod, running the wire out the bottom. This method will work with any tweeter, but some are easier than others so you may have to get creative. Now mount the tweeter pod back on the door and connect the tweeter wires that come from the crossover to the wires comming out of the tweeter pod.
The rear coaxial type 5 x 7 or 6 x 8 speakers will drop right in to the stock location from the top of the rear deck lid, and remember to connect them to the stock tweeter wires (gray 2 pin plug).
Once all the speakers are installed, mount the amps in the desired location and make all power/ground/remote/RCA connections. Make sure that the amp ground wires are the same guage wire as the power wire, and they should be kept as short as possible and need to grounded together in one common location. Once all those connection are made you will need to hook up the 4 pairs of speaker wires to the 4 channel amp. Using a 9 volt battery or a 12 volt power drill battery touch the positive and negative ends of one of the speaker wires to the terminals of the battery to "pop" the speaker. This will allow you to hear which speaker the wire is connected to so you can connect it to the proper output of the amplifier. Repeat this step for the remaining 3 speaker wires.
At this time you can connect the power cable to the battery, and turn the system on and check to make sure everything is working properly. Set the crossovers on the 4 channel amp to about 80htz high pass, and the sub amp should be set to about 80 htz low pass, and the gains should be set to about half way to start with. Make any final adjustments to get what you think is the best sound.
This may sound like a lot of work, but I've been a MECP certified installer for 13 years and can tell you that it is by far the fastest and easiest way to replace the Mach 460 system. An experieced installer should be able to complete this install in about 3-4 hours. I hope this helps and good luck!!
Also, I never solder wires with the exception of heavy guage remote start wires. Just use a good set of Klien crimpers and proper sized butt connectors.