If you're not interested in putting in the effort to do it the truly "right" way (soil analysis, different fert formulations at the right times of year, etc), why don't you just ask the neighbor with the "nice lush dark green" lawn what they use and when they use it? At least that'll put you closer to the ballpark than random suggestions from around the country...
PS: Unless you just want to fertilize whatever waterway your runoff eventually ends up in, do not fertilize just before a "week of rain"! (Or for that matter, even one day of heavy rain.)
PPS: Beware package label instructions, consumer lawn care product instructions always tell you to use more than you really should.
PPPS: If you really want a "nice" lawn over the long haul, it's going to take some effort. "Lawns" are not a natural phenomenon and need at least a certain amount of regular maintenance. If nothing else, Google up your county's ag extension office website. Unless you live literally out in the middle of the wheat fields (or fields of whatever it is they grow in your part of the world), it will probably have a section on lawn care and even if you don't end up doing most of what they suggest, you'll be better off with that than the generic instructions from companies more interested in selling you "product" than anything else, let alone, God forbid, relying on advice from 95% of the employees in the lawn/garden sections at a box stores or anything like that...