Probably can't give you the exact history as the FAL was used by something like 93 coutries as their official battle rifle. It and the HK G3 armed most of the free world for something like 30 years. It can still be found in some locales.
The FAL series of rifles falls basically into three groupings. The original military rifles (FN mfg'd and licensee), there were many, many variants as FN would do most anything reasonable to obtain a contract. Some variants would include full-auto or semi-auto, wood or synthetic furniture, barrel weights and lengths, metric, inch or Israeli style etc. Original FN and Browning (USA importer) FALs usually start at around $4k and all USA-legal FALs are grandfathered in as the BATF considers these as Title II firearms.
The second grouping would be newly manufactured FALs. This grouping would include DSA (www.dsarms.com), Entreprise (www.entreprise.com) and Hesse (www.hessearms.com). DSA has a sterling reputation in the FAL community while the others don't. DSAs start at around $1300 and the others start at a lower price (don't know offhand).
The third grouping is the kit rifles. These are rifles or carbines built on Imbel, Hesse, or Entreprise receivers. Fully built rifles start at around $600. This class generally includes the Century Arms rifles, gunsmith-built rifles and do-it-yourself parts kits. The best receiver by far is the Imbel. It is a Brazillian receiver made on FN-licensed machinery. The parts kits that you see advertised are all ex-military rifles that have been broken-down into parts, less receiver, for importation.
The only way to tell any sort of history of your FAL is if you have a scarce Browning import (G series or GL series FAL). Most likely yours is a kit as that is the majority of FALs out there. One clue is if it's an Israeli style then it was used in...Israel
. Watch out for the Ishapore FALs. They were reverse engineered when India was too cheap to purchase an FN license. These parts don't really fit on any other FALs.
Well, that is about as concise as I can get it. If you have any questions, fire away or go over to falfiles(url posted above).