+1 On looking up, getting on, and following Randy's schedule.
Now... Questions...
What's your budget? How "fast" do you want the backyard looking good? Obviously this winter is out, but do you want perfection by Summer or is "looks remarkably better than now this time next year" more your speed?
For this winter, depending on how severe it gets mow as needed until the first frost/freeze puts the St. A into dormancy. Then in the early spring, you'll want to hit the yard with a pre-emergent herbicide to take care of the summer weeds before they come up. Some here fret over winter and spring weeds, but I really don't fret over them. Winter and springtime weeds have a definite upper temp range that they just won't tolerate and they'll die off on their own. Additionally they won't be huge fans of being mowed regularly as the St. A breaks dormancy.
I'd say get on Randy's fertilizer and watering schedules then the most important thing you can do is let the grass grow tall and mow it high and often. Do that, get the turf good and thick, and you won't have to worry about annual weeds in the future. They will not punch through a dense turf.