If you are looking for something that is going to come in a ways under a grand you need to look towards the Ruger Mini 30. I have seen them at gun shows for as low at 600. Now that is not new of course. A new one will set you back about 800-900$. That is not bad considering a standard model M1A is going to set you back around 1,300 new.
As for an FN FAL forget about it. Even if you could find one, an FN FAL would be more than you are looking to spend. The knock off brands like Century, can be found for about 600-900. However, I would advise you to steer clear of the Century FAL's. Their quality control is hit or miss. I have seen some Century FALs that shoot flawlessly, and then I have seen others that looked like they were put together by a blind woman, they shot like it too. There are a lot of issues with Century and how they go about manufacturing their FALs. They tend to use mix and match parts.
DSA makes good rifles, but they are a bit out of your price range. The cheapest I have seen a standard model was a grand used. However, if you can find one for that cheap, snatch it up. The DSA SA58 is an outstanding shooter. It is one of the most intimidating rifles in my collection. When you hold it, you feel like you have an implement of war in your hands. There is no mistaking it's power.
In the end, if I were in your place, I would try to find a used Ruger Mini 30. It is cheap, it shoots pretty good, there are tons of websites out there for parts, magazines and accessories and the rifle is reliable. Ruger is a good company too. They do not have an official life time warranty due to all the restrictions that vary from state to state, however I have never heard of a case where someone was turned down by Ruger for replacement or repair. A few years ago I had a problem with a Ruger P89 9mm that had been though hell and back. I sent it to Ruger, they ended up replacing my P89 with a new one. They have one of the best customer service reputations in the business. The Mini 30 might not be the most accurate of the bunch, but it will get the job done.