Frankly, by far the most effective and safe weedkiller (cheapest too!) is the human brain. Redefine them as "biodiversity" and remind yourself they keep the lawn green during droughts and wintertime, and just live with them.
Honestly really truly, there is nothing wrong with a weedy lawn (with the exception of a *few* weeds like thistles or sand bur or things like that).
If you really, really want to poison things, then if your weeds are mainly annuals (crabgrass, etc) you can use corn gluten (there are various brand names) which will substantially inhibit seed germination if you put it on at the right time of year in early spring; it is pretty totally harmless and also acts as a mild nitrogenous fertilizer.
You want to kill perennial weeds, either hand-weed them persistantly, or take your chances with anything coming in a bottle that says "broadleaf weedkiller" (be sure to follow directions *exactly*)
Good luck, have fun, learn to appreciate 'weeds'

,
Pat