I'd spray all the weeds with a weed and grass killer (not Roundup). Just get the cheap stuff at Walmart, Ace, Lowes or HD, etc. Works great and costs much less.

You can chop and clear the dead weeds if you want to but it would be easier to just have the bobcat clear the weeds while doing the grading and site preparation. As long as you've got the bobcat, use it. Lots faster and easier than pulling or chopping weeds.

Are you doing a sprinkler system? You should be. Once the prep is done, put in the sprinklers. Then sod before the weeds grow again. If you're not going to lay sod then you may have to do more work to prepare for planting grass seed or hydroseeding.