An FAL is a fantastically fun rifle to shoot… along with a Garand, I think one should due in everyone's safe. I also also appreciate just how simple they are to maintain. The design is brilliant. A factory rifle, or a quality build, is utterly reliable and "infantry proof."
I would recommend picking up an older DSA (built with military STG58 kits), or an Springfield SAR-48 (also consider ban era SAR-4800).
There are a ton of "bubba" builds out there… be careful. Building an FAL isn't rocket science, but much more intensive than building an AR. Receivers and kits were once readily available for cheap, therefor home builds were/are not uncommon. I had the displeasure of picking up a couple guns that were serious basket cases that needed a complete rebuild before I learned better.
The comments about achieving constant 1 MOA with an FAL are laughable (but anything is possible on the internet!). I recall that that there was a guy that put a ton of time and $$$ to build his "space guns" capable of 1 MOA accuracy… he got close, but it required significant modifications that I suspect would shave degraded the positive attributes of the platform.
One should expect 2-4 MOA from a quality FAL with decent sights (I prefer para rest sight w/ A2 type apertures), I would be THRILLED with a rifle that constantly achieved 2 MOA.
If you want a highly accurate retro .308, and G3 type platform is far superior in that respect, but the G3 ergonomics and cleaning/maintenance of the platform falls short of the FAL. That said, I am always pleasantly surprised by how accurate my Springfield SAR-3 (Greek HK-91) with factory German Hensoldt scope. Fun on the bench.