I would rake up all the visible seeds and then start a regular weeding schedule.

That's what I would probably do, too. I'm impatient. But lots of seeds would still be there, and find it convenient to sprout right where I dug holes to put plants/seeds. It sounds like you have the patience to do exactly what you said, but easier. Water it, let whatever sprouts grow a bit, smother it again.

You're still going to have weeds sprout no matter what you do, but I think your plan is good. I like to pull whatever weeds I see daily so it's never a chore. I just lay them in the sun where they were to cook, no need to cart them around. Discovered I have no desire to go out with the sole purpose of weeding.

Now that I wrote all that, I wonder, are you trying to make a new lawn or flower/veggie bed?

I found, a long time ago, that "weed" seeds are so fine that the tines of a rake not only do not move them but more often then not will cover them with soil so they germinate better. Backin those days when I did till I would till the soil, wait a week and till again to kill any "weed" seeds that did germinate (watering if necesary), and maybe doing that again. What you do depends on what use this area is to be put to. If a garden you may well be able to lay down a good mulch (maybe newspaper or cardboard first) and plant. If a lawn maybe till twice, or more a week or more apart before laying sod or maybe seeding. Seeding turf grass might be best done in early fall when it is cooler and, usually, wetter.

Thanks for the helpful responses! I will start tomorrow and give you an update in a couple of weeks.