re: New house, neglected yard. I don't even know where to start.

You could go about this the easy way or the fun, lawn geek way. Honestly, I'd just kill it, till it, sod it, then put down a fertilizer that's high in phosphorus like a 15-15-15. Ewing has plenty to choose from. Make sure you keep it watered for the first couple of weeks, twice a day for several minutes at a time if you can. Then just put down a slow release fertilizer once or twice a year and make sure you don't scalp it with the mower.