The remote wire coming from your car harness should be the 12V accessory turn on line. It is used to turn on the radio when you start the car. It is different from the constant on 12V line which is always powered (to hold your radio memory, etc.) when your radio is not on. They both go from the car to your head unit. There is also an amp turn on which goes from your head unit to the amp - the amp does not need to be constantly on. This one turns on the amp (if you have one) when your radio turns on. First of all, you need a wiring harness. I got the following, but there are others from Metra and Scosche for 2003/2004 Mustang. I understand that different year Mustangs have a different setup and would require a slightly different wiring harness.
Check out the description of the pins on the crutchfield site. the larger connector connects to your radio harness on the car. The bare wires on the other side of the connector should match the color code of your aftermarket head unit wiring harness - just match them one to one and connect. The smaller second connector is used for your two Mach 460 sub amps. This requires your sub amp turn on wire coming from your aftermarket radio - again match the wire colors. The two RCA's will plug into your sub out of your aftermarket head unit. The reason that there are two of each is because you have two amps in your Mach 460 which both require audio signal (RCA plug) and amp turn on (blue/white wire). The voltage regulator would normally go between the aftermarket head unit sub turn on wire and both the sub amp turn on wires - just hook all three together. As far as I know, you should not need the regulator. Just try it first and if you don't hear the pop then you are ok.
I bought an aftermarket head unit from Crutchfield and have used the above wiring harness with some success. The only problem you might run into is that the way the Mach 460 system is configured: there are 4 tweeters (2 on the window sill and 2 in the rear) and 4 subs (2 on the door and 2 on the rear deck) The 4 tweeters are all individually powered from the OEM head unit and will be the same with aftermarket head unit with the aforemention wiring harness. However, the subs are powered really odd. One of your sub amps power both your door subs and the other powers both your deck subs! Don't ask me why! So the subs (if you want to keep the factory subs and speakers) are not stereo! Also, the tweeters are only high range. Therefore it is wise to pick an aftermarket headunit that can isolate only the high for the tweeters. Otherwise you will need bass blockers for all 4 tweeters. Hope that helps.