Welcome to FT, taigonwon!

You're off to a good start by checking out the wiki, and this Upgrades-specific page should explain things more clearly than the generic (and outdated) Awards page you quoted.

As gemac indicated, your best bet as a non-elite is to use mileage+copay for Award Upgrades. Just keep in mind that there are a couple of deep discount fares that are not eligible for Award Upgrades, and you can get the full details on different AA Inventory Classes here.

Once you get to GLD status, then you will be eligible to use sticker upgrades on all fares on 'domestic' routes, and again, this info is available on the Upgrades wiki page.