Old English fyrst "foremost, going before all others; chief, principal," also (though rarely) as an adverb, "at first, originally," superlative of fore; from Proto-Germanic *furista- "foremost" (source also of Old Saxon fuirst "first," Old High German furist, Old Norse fyrstr, Danish første, Old Frisian ferist, Middle Dutch vorste "prince," Dutch vorst "first," German Fürst "prince"), from PIE *pre-isto-, superlative of *pre-, from root *per- (1) "forward," hence "in front of, before, first, chief."
The usual Old English superlative word was not fyrst, but forma, which shows more clearly the connection to fore. Forma became Middle English firme "first, earliest," but this has not survived.
First aid is that given at the scene, pending the arrival of a doctor. First Lady as an informal title for the wife of a U.S. president was in use by 1908, short for First lady of the land (by 1863 with reference to the president's wife); the earlier title was simply Lady (1841). First name is attested from mid-13c. First base "a start" in any sense (1938) is a figurative use from baseball.
First-fruits is from late 14c. as "earliest productions of the soil;" 1590s as "first results" of any activity or endeavor. First love is from 1741 as "one's first experience of romantic love;" 1971 as "one's favorite occupation or pastime." First-floor is from 1660s as "story built on or just above the ground" (now U.S.); 1865 as "story built next above the ground."