I think Rhizo is imagining you've got more good plants with Old McDonald weeds, here-a-weed, there-a-weed... between a lot of "keepers." If it's more like that, it would be a matter of asking yourself, do I have the time to pull all of these plants up? Some people opt to remove the "good plants" to make it easier to smother large, unbroken areas. Wherever there's a gap in the smothering, weeds are, well, not suppressed, so if it's thin strips between good plants, smothering won't help much. As perspective, in my minds' eye, I see your beds as mostly devoid of desirable plants, with much space between those that would be "keepers." Although I wouldn't begrudge someone's use of chems to establish control, it would be preferable to me to smother where possible. I would define possible as any spot where I can completely cover a patch of weeds with newspaper or cardboard in large enough areas around existing plants so I could cover it with several inches of mulch without having the mulch wash "into" the existing plants. It's not that I have anything against using chems to establish control, but that's only part of the issue. If it's been lawn or neglected "flower bed," likely the soil does not have good tilth, fertility, drainage. Even this type of very basic lasagna can be incredibly helpful in all of these regards. If your dedication and determination extend as far, it's so easy to add other amendments as part of/when smothering. I like to put bagged lawnmower clippings under the paper in case it has seeds in it. (Then when the paper/cardboard contacts it, you've got a good green/brown thing composting under there.) Between the paper/cardboard and the mulch, one can add compost, leaves, whatever seed-free, easily decomposed organic matter is available. When you stick a shovel in later, that fall is OK if you want to add some shrubs/perennials, next year for summer annuals and anything more, you should be amazed by the difference. There's also an impatient form of smothering where one uses whatever they can keep in contact with the soil. A tarp or sheet of plastic, pieces of metal, the bags of mulch you will eventually use in that area, anything that will cover up the weeds until they die. After a time, you remove the cover and see if it's dead. Once you determine everything is, cover with mulch, compost, whatever your plan is, then start gardening. IME with using both methods many times, a smother layer of paper and the longer wait is worth it in the future. The quick-smother often results in the sprouting of many seeds that were at the surface but just hadn't decided to grow yet, especially right where you dig holes to add the plants that couldn't wait until next year, pretty much thwarting your efforts. With options, you can choose the best one, which you may decide is spraying. If so, putting a cardboard box upside-down on nearby plants can be helpful to avoid the mist from getting on them. Try to do when...

Yes, I do see the dandelion leaf in that shot now, I think. And the small dandelion plant in the last one. They very well could be multiple things there. I will look at some Erigeron species and compare them to what I have outside. Thank you very much, again!

The best weed control I've used in a vegetable garden is laying down newspaper and covering it with mulch...this is done right after planting while the pants are small. It's a very effective and organic weed control method.

It looks a lot like the Campanula Rapunculoides that I have in one concrete bounded area. It is a prolific seeder, as well as spreading by the roots - if I didn't keep it deadheaded, and it weren't confined by the concrete, it would be all over. I keep it because it is pretty and blooms all season, but it isn't something that I recommend to anyone else. It is considered a noxious invasive in many areas. Information Get rid of it now I would say! ETA: I overlooked that you already have identified creeping bellflower, but this new one still shares the characteristics: purple stem at the base, sideways running root, heart shaped leaves with stems in the early growth. Really does look like mine!