I have used the specialized stuff for this, I think it is from Ortho. Got it at HD or Lowe's. Have had some success with this product on about the same square footage of grass that you are talking about.
What part of the country are you in? I have found, from living in different areas, that weeds are more or less vigorous in different parts of the country. Living in MI, never had a problem with crabgrass, clover or oxalis. But the fungus was bad. Here in PA, lots of crabgrass and a little bit of clover and oxalis, but no fungus.
Another suggestion is digging up some or all of the grass, then seed or sod. I dug up a strip that is 5' x 20' because the grubs (Japanese beetles) destroyed it last summer. Seeded it on March 1 of this year and it is looking beautiful, with no weeds. This is a multi-year strategy, but it will give you a good result. Depends on how patient you are, and what your time horizon is for selling the house.
I'm taking the same approach with my shrubs. After 4 yrs of neglect from the previous owner, I had to chop back many shrubs severely. Some rebounded after the first year, but some needed 2 years to get them where I want them. Just about all of them are looking nice now, but it was ugly for a while. Again, the alternative is to dig them up and replace them. But in this case I chose to aggressively prune vs. replacing.
