HELP

Okay....so we moved into our house here on Post and we LOVE the house, but the YARD IS A DISASTER! The people that lived here before us did not take care of a thing! I swear we have more weeds than grass, and then the grass we do have looks like its pretty much dead. So here is my question to all you homeowners or anyone that knows anything about lawns. Where do I even start?!?! I have never had to deal with a lawn like this before, and because i know we will most likely be moving in a few years, and the house isn't actually "ours" I don't want to spend a whole lot of money, but I also want a decent looking yard and somewhere I can let my kids play and not worry about a weed infested mess! Now I say decent looking because I know I can't get it perfect and because I don't want to spend a fortune on this thing, but seriously this yard is embarrassing! I put a weed killer down, and I have noticed some of the weeds wilting.....but seriously there are so many I don't think applying a weed killer is going to work, and I can't even think about seeding this yard until we get rid of these weeds, and so I'm wondering is there no hope??? So here are a few pictures of the yard.....Don't judge...well, actually you can judge, because I judge the people that lived here before me, I mean seiously!! So any advice would be MUCH appreciated!

I have been watering this thing for over a week and it still looks like this...... UGH

here is a close up of a section where its pretty much all weeds...... Scary!

and this is even after i put the weed killer on it!