Three good options under or around $1000
H&K G3: the U.S. company JLD Enterprises bought a bunch of HK tooling from Europe, and is producing US-made clones of the G3 service rifle. These are getting great word of mouth on THR. Not everyone likes the G3, but those who do have been very pleased with the PTR-91. These can be found from the mid $700s NIB in some places, and come in quite a few variants. Run a "Search" on THR under "PTR-91" to read all the reviews.
FAL: I believe DSA has a few models right at the end of your budget, ditto on "Search".
M1 in .308: For around $400 you can buy an M1 Garand from the Civilian Marksmanship program, and for another $200 can have it rebarreled to .308. Get one of the non-collectible ones with a worn-out barrel. For far under $1000 you can have it refurbished, tuned, and rebarreled to .308 by a good gunsmith, and it'll be (in many ways) better than a $1,400 Springfield M1A (M14 copy)
Just a few ideas,
-MV