Here's what I would do and have done.
As soon as possible get and spray this pre-emergent on your yard. With the winter weather coming, you may have a few more days but mid-next week at the latest.
https://www.amazon.com/dp/B00OXD2CKG?ref=ppx_yo2ov_dt_b_fed_asin_titleThen, just leave your yard alone for the next couple of months. Whatever grows, grows. You can't do much about it anyway. At that point (late March/early April) nuke the ENTIRE yard with Glyphosate. You can get the generic product at Tractor Supply or online. It will die within a week. The reason you don't want to do that now is weeds will grow in February and March.
Till up the yard -- you can get one of those garden weasels at Home Depot or rent a machine; no need for serious tilling just break up the dirt a little -- and spread seed. I buy my seed online at hancockseed.com, but if you have a local seed store go there. You're limited to what grasses come in seeds but with that yard getting plenty of sun, I'd go with bermuda. It looks like you have some there anyway.
Water the heck out of it. Good seed will start to sprout in 3-5 days. The only caveat is if it doesn't get too hot in April you might need to reapply in May or even June. Bermuda seed can withstand really hot temps but it doesn't seem to want to get out of bed until its 90. I had a buddy like that!
If you really want to go sod, no problem. Just go with these directions and lay down the sod. You'll need to clear out all the dead grass first.