Kill 'em "once and for all?"

Not gonna happen. In part because seeds continue to blow in, birds will drop seeds in poop, and the existing soil seed bank wherein seeds sprout every time you disturb the soil.

That said, you can minimize weedy growth. Remove what you see as soon as you see it. If you miss some, don't let them seed. And apply 2 inches fresh mulch yearly.

Even a mulch may not stop new "weeds" from seeds deposited by birds from growing, but a good mulch that keeps any "weed" seeds in the soil from getting access to sunlight will help keep those from growing. 2 inches is a bare minimum and if I can only put that amount on I will cover the soil first with newspaper as a "weed" block.
Some things, such as Quack Grass, will grow through any mulch you put down unless you first dig out all the rhizomes in the soil and put down a barrier that will keep new rhizomes from invading.