Normally you would mow new grass a bit shorter, and often, 1-2 times per week once it reaches 3 inches. This will encourage tillering and maturation. Even for a low maintenace type situation I would still start off mowing like this to get a full thick stand of grass. For the last mow of the year you want to mow it pretty close. Leaving it long can increase the risk and damage from snow mold, and all those long blades will get matted down and inhibit new grow in the spring.

fall (about a month before it usually freezes) is the best time to fertilize your lawn it prevent disease and weeds.