I'm in Ohio, total lawn is about 15,000 sq ft. My approach is to do enough work on the lawn so it looks okay, but not to go crazy over it. It seems the first 20% of the work gives about 80% of the results of a full-court press, and that's enough for me. I prefer to minimize use of chemicals, but will resort to them when they are needed. That generally means I avoid "broadcast" use of them on the hose-end sprayer, but will spot treat with a pump sprayer.
Violets: I leave them alone. The lawn seems to have fought them to a standstill and I can live with the ones that are still out there. Pretty little blooms this time of year and they stay green with the grass so aren't unsightly from a distance.
Dandelions: Same as braumeister: Pluck off the flowers/seeds and spray the individual weed. Any of the commercial broadleaf weed killers seem to work well. You might have to do this fairly frequently at first: if a plant is still putting out flowers a week after you sprayed, then you missed it. Pluck and spray it unless the leaves are all twisted and it's in its death agony, then just pluck the flowers.
The biggest weed problem I've got is creeping charlie: It is invasive and will crowd out my lawn.
I can keep most weeds at bay by keeping the grass healthy. I don't mow it short and I give it enough fertilizer (when the soil has enough nitrogen the clover also won't get much traction).
By hand-spraying and staying on top of things you can really cut down on chemical use. I need 1- 1.5 oz of the concentrate to tackle my yard by hand-spraying individual weeds. My neighbors with the "Chemlawn" service are probably using 20 times that amount (based on the odor).
And also are there any good web sites for someone like me who wants to learn more about taking care of a lawn without spending a lot of time on it?
The local agricultural extension office of the USDA (probably run through your state public university) will often have good guidance based on local conditions.