Not sure what “nontoxic” products you’re looking at or what exactly you’re trying to accomplish. If you use things like vinegar or salt or boiling water, it will kill everything, not just the weed (and also affect the soil and earthworms and other soil critters). Take a look at the labels on some selective herbicides that kill weeds but not grass (for example, WeedBGon) and read the safety information. Maybe you’re ok with using a product that dries in a certain amount of time and then is harmless to animals? Maybe not.
Read the herbicide info in the cool season maintenance guide here:
If you know the weeds, you can target them with the correct killer. You can spot spray, you don’t have to spray everything. If you use them, you should follow all the protective clothing guidelines and other precautions (like no wind, temperature below such and such).
But if you’re not comfortable using herbicides, that fine. It just means you probably need to live with the weeds. And there’s nothing wrong with that. You have clover. Nothing wrong with clover. It’s even helps provide nitrogen to the soil. But it does spread and and can choke out your grass. If you’re trying to have a grass only lawn, you probably want to get rid of it and the way to do that is with a product that has triclopyr. It’s your choice: live with clover or use triclopyr maybe once or twice a year.
For your borders, just pull weeds out manually. Use mulch.