I believe it is generally qualified by being the first permanent/successful English settlement. Or the first permanent/successful settlement in what would be come the 13 colonies (Florida being the 27th state to join the union).

But even what you mention is not quite true. St. Augustine was founded after the French attempted to settle the region. In 1562 and 1564, the French set up Charlesfort in South Carolina and two years later near where Jacksonville would eventually be they founded Fort Caroline. St. Augustine was founded after the Spanish sacked the French in 1565.

But long before you had Jamestown you also had Santa Elena a settlement founded by the Spanish roughly where Charlesfort had been. It existed for roughly twenty years before the colonists left, many moving south to St. Augustine.

So unless you qualify Jamestown as the first successful/permanent it doesn't really count as being the first in what would become the 13 colonies since Charlesfort and then Santa Elena and then even Roanoke preceded Jamestown in what would become the 13 colonies.

Also don't forget Santa Fe, NM, founded in 1598 was both a successful and permanent settlement almost ten years before Jamestown. It also has the title of oldest capital in the union since it was a provincial capital in the Spanish colonial system.

So Jamestown was not the first permanent/successful settlement unless you qualify it by saying the first English settlement in what would become the 13 colonies.