The more plants you can decide that you want, the fewer 'weeds' you'll have to control. We embrace diversity and variety in other areas of life, so why not in our landscaping? Let the 'bonus plants' alone if they aren't on the noxious weeds list in your state. If you simply must get picky about which plants may survive on your place, pull them by hand. If they are annual or biennial plants (that only live one or two years), pulling them before they produce seed (which is usually after the flowers wilt and fall off, or when the inflorescence or 'seed head' of grasses turns a wheat straw color) will eventually reduce them down to a level you can live with.
Prevent plants from growing where you don't want them in the first place! If plants are growing in sidewalk cracks, for example, keep those cracks clean of dirt to prevent seeds from germinating there. You can also use mulch thickness (at least 3 inches deep) and regular cleaning of that mulch (with a leaf blower and/or rake) to keep dust from accumulating between the mulch particles and creating seed beds for the 'weeds'. That way, seeds falling on the mulch will get eaten or eventually expire before they sprout. If they do sprout, their root won't reach nourishing soil before the seed runs out of energy to grow more root. Also, seeds in the soil below the mulch won't be able to get their first stem and leaves up above the mulch layer and into energy giving sunlight before the seed runs out of stored carbs either.
But, don't use 'weed barrier' below your mulch! If you have any plants that you do want to live growing in or around the mulched area, that weed barrier will also reduce the gas exchange (oxygen down from the atmosphere and carbon dioxide up from the respiring roots and other critters in the soil) and can even prevent water from spreading as it should to encourage a healthy root system (roots can't grow in dry soil, so you wind up with weak roots that can't support your plants if you only water them up by the trunk or stem). Weed barrier also only works for a year or two before wind and water deposits more soil on top of it, unless of course, you keep your mulch clean as I mentioned before. It's easier to rake and stir mulch to keep it clean without a weed barrier below it to snag your rake on.
Don't spray anything that will kill plants (no matter how 'organic' or 'natural' it is) on places in your landscaping where you want specific plants to grow. In fact, these natural and organic 'weed killers' are even less selective than the commercial sprays and will kill everything that is weak enough to succumb to them. Even perennial plants can be killed or at least stressed by this stuff. You can eventually kill even your perennial trees by spraying any kind of herbicide on plants that are in their root zone (from the trunk to several feet past the drip line of the canopy). Trees and shrubs are 'broadleaf plants' too and will be affected by any weed killer that targets broadleaf weeds. Even the most selective spray becomes non-selective if you put down more than the label says to or apply it more often.
So, be careful with this stuff, even the 'safe' stuff like vinegar and vodka. If you use it, keep away from perennials that you want, even and especially the neighbors ones, unless you want a fight on your hands when their prize rose bush along the border with your yard starts mysteriously dying. You really are better off just pulling the 'weeds' by hand or better yet, learning to appreciate them for what beauty they have.