1000 dollars.
You don't need a rig, all you need is a good GPU. There are ones specifically made for coin mining, check out Butterfly labs.
Also, it'd be within your best interest to find another coin. Litecoin is valuable, but it's much more worth your time mining something like Worldcoin, Nextcoin, or Megacoin.
Seriously though, mining isn't always worth it, and it takes up a forgetton of energy. It's much more likely that you'll have your money wasted than spent well.