Generally, you have to go with what the locals call themselves. The names of foreign countries and their associated demonyms are often transliterated or reinterpreted versions of the original—or altogether fabricated because the original is unknown. As with any term in any language, the most popular wins.
These five suffixes seem by far the most common:
Other suffixes listed in the Wikipedia article such as -ard as in Spaniard and -onian as in Newportonian are rarer and sound a little more old-fashioned. If you need to coin a new demonym, such as for a novel, then I would use one of the more common suffixes and leave it at that. People from Earth are often called Earthlings, but all of the other Solar planetary demonyms end in -an, including other names for Earthfolk such as Terrans, Tellurians, and in Futurama, Earthicans.
Speaking of -folk, it’s best left to things with a folksy sort of feel—Tolkien’s Shirefolk, for instance, parallels townsfolk, gentlefolk, menfolk, that sort of thing.