Using a 3-wire alternator
A 3-wire alternator differs from a 1-wire alternator in that the 3-wire alternator has an external source of excitement to the alternator.
In practical terms, this means that a 3-wire alternator is typically able to begin providing power sooner at low RPM, compared to a 1-wire version. A car with a 1-wire alternator may not output enough power at idle or low RPM for extended use. The battery will be discharged faster, and with extended idling, may actually go flat. That's why police cars don't have 1-wire alternators. On the other hand, if you have a race car that rarely idles, the simplicity of a 1-wire alternator may be attractive.
The tradeoff is that wiring is somewhat more complex for the 3-wire setup. But not much.
Using a 3-wire alternator is easy with the InfinityBox system and the GMPP harness. InfinityBox has a Wiring note. This works well if the alternator wants to see 12V. But many modern alternators want to see a lower voltage, and can be damaged by just sending 12V to the exciter terminal.
If you are using the GMPP harness, and a GM alternator that needs the less-than-12V exciter, the harness has an connector on the harness to drive the alternator. The correct voltage from the engine ECU fusebox comes with the controller kit. You may need to re-terminate the connector to match your alternator, but this will typically be a great solution if you have such an alternator.
If you choose a 1-wire alternator, the GMPP harness output should be taped off so it can't accidentally short to ground.
There are too many possible connections to document them all, but in general, connect the GMPP alternator wire to the "S" connector, or to the "2" connector. Check with your local alternator rebuilder with your alternator in hand to be sure!
The bottom line
You'll need to decide which style you want, and if your driving profile will tolerate a 1-wire alternator. With a 1-wire, you only connect a big cable to the alternator battery stud and you're done. With a 3-wire, you also need to connect a small wire from the GMPP harness (assuming you are using an LS-series engine) to the appropriate connector on the alternator.
One last point- though the alternators with more than just a battery cable stud are all called "3-wire" alternators, they can have 2,3,4 or a different number of terminals. Don't take it literally when you inspect your alternator!