Facebook ads can get you great installs, and very targetted too...but can go upto $1.50 CPA. If you want lower costs look at Millenial Media or Tapjoy.
I would put the $1000 purely into getting direct downloads as opposed to any brand/awareness building campaigns.
I don't think Marketers should work with a fixed budget like you have described. Check out some of the applications on octopus.org, most of them have free trials and free functionality. See what works before you spend any serious money.