Arizona Response Systems is the best guy to build a FAL in the US, better than what i make and have used anyway. DSA sells decent pre-made rifles, especially their StG 58 line. however, this will be very near the top of your budget. used rifles are floating around but not much cheaper. be wary of mix master home builds because locking shoulder and barrel torque need to be precise or you will have a dangerous situation with pressure.
PTR makes most of the parts for the Century CETME and C93 after the surplus from Malaysia, FMP, Spain, and Portugal dried up for mass manufacturing. Century contracts with several shops to manufacture them (I started out making Galil's for Century back when i first started gunsmithing). the in-house Century assembled ones can be suspicious.
M1A/M14 are towards the top of your budget, very few semi-auto .308's are under $1500 significantly enough to be a "good deal" that isn't a used rifle or surplus. the various G3 pattern rifles would be the best bet, and if you don't like the ergonomics you can customize them significantly with aftermarket parts.
.308 "Navy" M1 Garand rifles are available relatively inexpensively and are kind of interesting.
edit: also should mention that CDNN bought out a lot of Remington Defense and Remington Firearms parts, as well as a windfall from DPMS and Mossberg and Remington's parts manufacturing depts (which are OEM for AR-15 / AR-10 small parts and even things like AR barrels and stuff). so it's possible to get the essentials of a DPMS-compatible AR-10 .308 build going for less cost by parting it together from CDNN and other sources like Brownell's. if you're going to do this, stick with "DPMS LR-308" compatible parts since they are the most popular and most "AR-15" like. CDNN has been clearancing out there AR stuff for a while now.