Moss isn't a problem-at least it's green and under control. The 'weeds' are dandelions (which I can pull if I have to), creeping Charlie (at least that's what my mother called it; kinds of a round leafed vine that weaves through the grass) and the ubiquitous maple seedlings which I've been pulling out of my garden beds by the hundreds, and don't have the time or the patience to pull from the lawn. In all honesty, the weeds aren't the big deal so much as I want to fertilize the lawn and overseed it ... I can keep the girls contained while I reseed but how to evenly fertilize without hurting them??
Before you start throwing money at fertilizer get a soil test. UConn has a soil testing lab and the CT Ag Experiment station can test your soil. Prices are reasonable. The nice thing is that after the soil test you will know how much fertilizer and lime you will need to put down to care for your lawn. If you can plan your fertilizer application to a time just before a couple days of a slow soaking rain, the fertilizer granules should dissolve adequately. N, P, and K are highly soluble.