you should be able to build a basic shooter with iron sights for around $600 if your real patient... by that I mean you need to wait for all the parts to come together for your budget.
You can find stripped lowers for $110 and up.. but you'll have an easier time if you spend a little more.. PK has a Roggio Arsenal Stripped AR15 Lower for $135 right now.. this requires a FFL as it's the only part of the gun with a SN, so it's technically 'the gun'
PK Firearms | Online Store
Then the sky is the limit for building the rest.
Lower parts kits (trigger group, bolt catch, mag release, safety/takedown pins and detents) range from around $75 and up. I was reccomended the DPMS kit from a fellow member here, and have put three lowers together.. they all functioned perfectly so far with no machining/filing or major fiting issues
Your buttstock can range from $75 bucks or so (say for a standard A2 with buffer tube, or a real basic telescoping A4 collapsable) all the way up to $200-350 for the latest and greatest supercalafragalistic stuff..
Your Uppers again have a HUGE range.. but a basic flat top (m4-like) or carry handle (A2-like) can be had (with some patience) for $450 or so...
OR
after you get your stripped lower you can wait the 16 weeks and pick up a complete kit (minus the stripped reciever) from Del ton for $485 and up...
Del-Ton, Inc. AR-15 Rifle Kits - 16"
Or there is always cruising the AR15.com forums in the equipment exchange section for other guys selling parts/setups.