Answer: The best management solution is to spread a 4-5" thick layer or organic mulch over the area to suppress weeds. Without sunlight, weed seeds won't be able to germinate. Spread it now and then dig it into the soil prior to seeding or sodding your lawn.
Or, you can simply knock down or hoe down the weeds that appear. Go after the weeds that are flowering first - you want to stop the flowering/seed producing stage. If they go to seed, you'll end up with dozens, if not hundreds of weeds in the area. I'd knock them down with a hoe and then rake them up. Don't just knock them down and allow them to lay there - they could drop seeds. If you have some persistent weeds, you can use a contact herbicide such as Round-Up, sprayed directly on individual weeds. You'll still want to rake or pull them up after they're dead (so your yard doesn't look like a weed patch). It may be a lot of work now but if you keep the area as weed-free as possible before sodding or sowing, you'll have fewer weeds to deal with after your new lawns are installed. Best wishes with your landscape!
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