How big of an inverter you need depends solely on the amp requirements of the things you plug into it. Once you know the maximum current draw you'll ever use, you can then determine what size inverter you need. Once you know the current draw, and the total number of amps you'll draw between fully recharging the battery, you can then determine what size battery you need. This assumes running off an auxiliary battery.
If you're running the inverter off the vehicle's electrical system while the vehicle is running, then the high amp draws of a fully loaded 1500 Watt inverter or a seriously large stereo amplifier will draw more power directly from the alternator, in which case a Big Three Upgrade is a good idea. 1500 Watts is 125 amps DC, so you'll need to ensure the Big Three cables can handle 125 amps.
For the engine-to-ground, most vehicles are already directly bolted to the chassis ground, so adding another wire is not even needed, and in some cases can cause a ground loop, so make sure you know what you're doing on that one.
The battery-negative-to-ground, 8 AWG cable is sufficient, and you probably already have at least 4 AWG for that.
For the alternator-to-battery (or more common, the alternator-to-starter-to-battery) best is 2 AWG, but 4 AWG will still provide the required number of amps up to a 10 feet of cable.
Some vehicles come with puny cables, some do not. If they don't need replacing, then then don't need replacing.
Your friend who thinks the Big Three Upgrade enables him to run a 1500 Watt inverter is confused. You will simply not draw enough amps from a 1500 Watt inverter to make the Big Three Upgrade a factor. The Big Three Upgrade comes into play when you have something like a high powered stereo amplifier that draws 200 or 300 amps from the system.
Mainly, though, it depends on how you have the inverter connected to the system, whether it's connected directly to the 12-volt charging system (requires properly sized alternator and the appropriate Big Three Upgrade), or to the cranking battery (not smart at all), or to an auxiliary house bank (best).
If you use a house bank, the Big Three Upgrade (if needed) can play a factor in the recharging of the batteries, depending on how far you draw them down and how much charging current the alternator will feed them. If the alternator will be feeding them 70, 80, 90 amps for a long period (4 or 5 hours) before the amps begin to fall off, then you're really taxing the alternator and the wiring harness, and a high amp alternator and larger wiring may be needed. But for a 1500 Watt inverter, unless you plan on running 1500 Watts continuously for hours at a time, you're good to go with no modifications necessary, frankly.
But, you're right, 1500 Watts off a single battery is a lot, unless it's a really, really high amp hour battery, like a forklift battery or something. 1500 Watts will drain a cranking battery in a matter of minutes. Reserve Capacity (RC) is the number of minutes a fully charged battery at 80° F will discharge 25 amps until the battery drops below 10.5 volts. A typical cranking battery for a Chevy would be a Duralast 24DT-DLG 800 CCA battery. It has a RC of 115 minutes, which means at a 25 amp draw the battery will be dead in 115 minutes. At 125 amps, the battery will be dead in about 9 minutes.
I run a 1500 Watt inverter, but rarely get anywhere near the 1500 Watt mark. With the light, Espar, fridge, computer and external hard drives, and the satellite DVR box and television going, I can draw as much as 22 amps or so (226 Watts). If I fire up the microwave, which is a lower power unit, the amp draw jumps to 50 or 60 amps (up to 720 Watts). I have a Dirt Devil 120 volt hand vac that draws 720 Watts. It's very rare that I'd want to run the Dirt Devil, the microwave and everything else all at the same time.
