In the Deep South, there are ALWAYS weeds. Weeds from long lived seeds present in the soil that may germinate several years later (nightshade), seeds that blow in on the breeze (dandelion and wild lettuces), seeds that are dropped by passing birds (sassafras, pokeweed), seeds that are transported in by squirrels (pecans, acorns); weed seeds have so many ways of getting into your garden that a "weed free zone" is not just a dream, but a hallucination.
That said, you don't have to keep up with ALL the weeds, just the most obnoxious. There are other Permies that give
bindweed the evil eye, but I can keep it under control by looking for its flowers and yanking it out before it has a chance to set
seed for another crop. Johnson grass is another weed with a fearsome reputation, but I usually let it get to a good size before I pull it -- it's a good fodder plant, so I want to pull it after it has put on some growth, but before it flowers. Most weeds have their seasonality, so if one kind is growing a little too well, maybe you do need to get out and suppress it before it can get a start and become established. The nitwits doing road construction in front of my property put down some straw for erosion control, but it was full of nightshade seeds

now I have to do a patrol and snuff out any nightshade seedlings before they can get established.
As far as specific suggestions, dandelions and crimson clover are not what you are looking for. Dandelions are a winter weed, and I have never seen them be able to crowd out anything else; crimson clover is a cool season annual, and comes next May, it will go to seed and be absent for the next 6 months. What might work?
--Oregano I have some thick stands of oregano, and although in a few places it does have some stuff growing up through it, it chokes out a lot of the possible competition.
--Mint Not nearly as good at choking out the competition as oregano, but it does spread faster.
--Cowpeas This is my first year trying this as a ground cover intended to fill in and smother the competition. I got too late a start, next year I need to seed them earlier, but I like the results so far and will keep at it.
--Chicory I like to spread chicory seed when I am doing my fall weeding. It is a good competitor in the cool weather and when it gets going, it can outcompete a lot of the more noxious weeds. Each nightshade seedling I dispatched today got a sprinkle of chicory seed to replace it.
I've made my peace with some "weeds". I know that henbit and Carolina geranium are going to show up every winter, so rather than get bothered by them, I just wait for them to get to good harvesting size and then I yank them for animal fodder. Every "weed" that you can find a useful purpose for is one less plant that you have to take pains to eradicate.