As already said, to do it easiest and best way grab a 12v rail off the battery, until you start going over a 1000w true rms class d amp, you will not need a cap, especially the fact these trucks have 2 batteries in them. there is some misinformation here, the class d doesnt shut off, its just a more efficient way of amplification compared to class a or ab amps, although it does have a higher thd and is really only useful for low frequency applications.
as far as wiring goes the bigger the better for 1kw total rms power, 4 guage will be fine, but bigger, the better.
you can hook straight to your battery, their will be a minimum residual power drain, but nothing more than all the other accessories in the vehicle that arent on a relay, the amp has its own internal switch, theres 2 ways this is done, one is a presence of a voltage on the rca interconnects, or high power inputs, or it will use a 12v remote switch either from a switch you can hook up or, almost all head units will have an amp remote line on the back of them for this purpose.
if you are using 2 memphis audio subs, (ive been out of the car audio scene for quite some time now) they used to be a premium sub, so i'm sure you are going to want to throw more than 100w at them, that build your own amp kit, will not even come close to satisfying your need. and honestly i wouldnt doubt it if that amp couldnt handle the massive continuous power output needed for driving subs. if you havent decided on an amp yet, if you can find a classic jbl bp600.1 or 1200.1 they are the best performing value class D you can get. or if you are going to spend some money, grab an mmats class d amp, there is no better performing amp period.