From FF7, the Ancients' original name, Cetra, could come from the Latin 'cetera', meaning 'others'... the Cetra were the 'other' race of people who originally populated the Earth.
Chocobos might have gotten their name from a chocolate candy which sold in Japan a few years back (and is still popular). It was called "Chocoballs" and had a picture of a bird on the front. But unfortunately the bird looks nothing like the familiar yellow chocobo that we all know and love... ^_^
Espers: Esper itself is a made-up word, but it might be related to "hope" (from French; 'a hope' is 'un espoir') or someone who has extra-sensory perception (an ESP-er)... The Squaresoft Repository notes that the word was used in this connotation in a story called "The Demolished Man", by Alfred Bester. It was written in serial form in Galaxy magazine. It was also mentioned in "Solar Lottery" by Philip K. Dick, and "Highways In Hiding" by George O. Smith. A comic series called "Espers" was also published.
Genome (FF9): From A.L.: "Genome is a biological term used to describe the genetic information in a somatic cell."
Guado (FF10): Moogle Fan tells me that it's Italian for "woad", a type of plant. Since the Guado look very plant-like indeed, it probably makes sense. And Mush Mordan adds: "The woadwose were supposed to be a humanoid race that tended the forests in ancient anglo myths, much like ents, they looked like humans made from bushes and bark etc."
Hiryuu literally means "flying dragon" in Japanese.
Moogles are called "Moguri" (or "Mogli") in Japanese, and that comes from a combination of the Japanese words "mogura" (mole) and "koumori" (bat). And doesn't Mog look like a mole with little bat wings? :)
Moomba: Moogle Fan sent in a site that says as follows: "Moomba" is a 40,000-year-old Australian aboriginal word, for "let's get together and have fun". Rather apt, I think. 8-)
Shumi: Moogle Fan says this is Japanese for "hobby", "tastes", or "preferences". Makes sense considering that they're named after their vocation.