One should always address the soil before tackling weed and plant issues.
I'm a firm believer that good soil = healthy plants = few diseases and little need for chemicals.
Every plant has a place in which it likes to grow, due to soil composition and climate. Once we understand and accept this principle, its a matter of deciding how to modify conditions to favor the plants we want while making it uncomfortable on the plants we don't want.
So, firstly, you need to discover what your soil is missing. You can either send a sample to a lab for a soil test or you can use your best judgement based on weeds you see that are thriving and a general knowledge of weather and soil conditions in your area. For instance, if you know you get more than 30-40 inches of rain per year, its very likely your soil is acidic and deficient in calcium. Moss is a great indicator of acid soil because it grows where nothing else will. Moss can grow equally well on the top of a brick, which is about what acidic, compacted soil amounts to. Other weeds can indicate other conditions: Yarrow can indicate potassium deficiency. Clover indicates nitrogen deficiency (since clover can fix its own nitrogen from the air). A simple search on google will generate many lists of indicator weeds and their theoretical meanings.
A soil test can help you determine what needs to be fixed, but a soil test is only as good as the sample you send in.
Yes, if you fix the soil, the weeds may flourish more, however if you've designed the soil composition properly, the grass you sow will out-compete the weeds.
Blanketing with weed killers will not address the underlying cause, which is nutritional, therefore the weeds will come right back once the toxin is gone.
See my answer here for more info about calcium, compaction, and moss.
And here for more info about competition between lawn species, particularly clover.