For now, I will be covering only the relevant bits and some history of the enemies/references in FO3.
http://fallout.wikia.com/wiki/Fallout:_A_Post_Nuclear_Role_Playing_Game#Mariposa_Military_Base Is a wiki that goes into detail of the majority of FO1 for those wishing a more in-depth thorough lore read.
First off, super mutants. Super mutants in FO1 were created by the FEV virus through accidental, then deliberate dippings in vats of the green goo. One of the first sentient creatures dipped into these vats was by an accident while searching the base with a band of people, this band consisted of Harold the Ghoul, some red shirts, and Richard Grey.
Richard Grey would transform into a blob of flesh that became known as The Master, which reached a pinnacle of intelligence and dipped those that stumbled into the Mariposa Military Base into the vats just as he was. Which birthed the first super mutants. A mutant that retained his intelligence, known only as The Lieutenant was put in charge of the Mariposa Military Base while The Master concocted a plan of forceful mutation, those unwilling to be mutated would be forced to not breed as they were not considered viable for the new future of the Wasteland.
The Master hides underneath a religion, and the confrontation by the Vault Dweller can be seen in this video: http://www.youtube.com/watch?v=1lbBa_3IXos&feature=related
The Master could be dealt with in a myriad of ways, from setting off a nuke in the basemant of the church, to dipping yourself in a vat and serving the Master/losing the game, to killing the Master in-combat, or convincing him to the futility of his plan after presenting a found report that super mutants are completely sterile and cannot sustain themselves without humans, this approach was used in the video above.
In FO3 I have yet to see an unifying force behind the Super Mutants, simply bands that seek to reproduce through dippings of captives. Intelligent Super Mutants are a result of a non-contaminated human (Enclave/Vault being prime candidates) due to not being exposed to a mutated FEV strain that is in the air that makes contaminated humans stupid super mutants.
Ghouls have been changed significantly in some ways from FO1-2 in FO3. In 1-2, they couldn't run, simply shuffle. Also, the "feral" ghouls of FO1-2 were Glowing Ones in the sewer that shuffled just like the others, but did use melee I cannot remember if they were cannibals or just mindless. The majority of ghouls were still sentient if hesitant about smoothies due to prejudices. The makings of ghouls are contradicting, but it's generally accepted that they're humans from one of the vaults that opened prematurely, being dosed in heavy radiation that wasn't just enough to kill them but did severely mutate them. Making them live for far longer then regular humans at the expense of their bodies.
http://www.youtube.com/watch?v=XLySGSRAhWo&feature=related Set the Not so Nice Ghoul.
http://www.youtube.com/watch?v=OJjYczaQdZ4&feature=related This is Harold, he's been present in each FO. He's the Oasis tree in FO3, in FO2 a tree began to grow out of his head, Harold speaks about the vault opening prematurely.
The Enclave did not exist in FO1, but did in FO2. This section will be expanded later.
The Brotherhood of Steel in FO1 is an organization that was concerned primarily about the preservation of technology, while recognizing the Super Mutant threat but not quite willing to attack the Mariposa Military Base without further reports. Similiar system of organization as present in FO3. The split in FO3 represents the more idealistic view of the BoS that Tactics was trying to show, with the Outcasts representing the true interests of the original BoS. Not the most nice people. They send the Vault Dweller to "The Glow" to prove his worth and allow him access to their outpost/technology. It was thought to be a suicide mission due to the very heavy radiated nature of the place. Resting there would result in death as well as playing chess with a certain computer in The Glow...
http://www.youtube.com/watch?v=kY-HecC5zMY&feature=related Initiate speaking about completing a quest to enter the BoS.
http://www.youtube.com/watch?v=Vgz92pMRPuc&feature=related Speaks of the purpose of the scribes.
Deathclaws in FO1 and FO3 differ in many ways, Deathclaws were dangerously quick and hard hitting in FO1, while in FO3 they are slow but hit even harder while standing upright primarily while the ones in FO1 were hunched over and brown. Also, they often lived in a family system of many offspring with a few advlts about in FO1.
If requested, I will further expand this to encompass any connections that have been missed or not clarified. Any errors or the like that are pointed out will be corrected and if any clarification is necessary, it shall be fixed accordingly as is reasonable.
Fallout 1 Intro: http://www.youtube.com/watch?v=EqiMS_0yto8
Fallout 1 Master Ending: http://www.youtube.com/watch?v=PfyqlMBeQFU
Fallout 1 (One possible ending): http://www.youtube.com/watch?v=jG_P086L5LU
Fallout 2 Intro: http://www.youtube.com/watch?v=jNKUfk-MgJw