This will be short and sweet.  There is no prehistory.
Columbus happened upon the islands on his second trip out in
1493.  He named them for the virgin St. Ursula.  They were
uninhabited.  Thereafter the islands became a hangout for
renegades.  Permanent settlements were made by English and
Dutch in the 17th century, the English eventually evicting
the Dutch.  The Danish West Indian-Guinea Company acquired
the islands piecemeal: St. Thomas in 1672, St. Jan in 1717,
and St. Croix in 1753.  The idea was to import slaves from
Africa and grow sugar cane for the Scandinavian sweet tooth.
The "Compagnie" issued paper money in 1717 and 1727.  They
were withdrawn shortly after issue, and today these notes
are either hyper-rare or non-existent.
First coins were struck in 1740, consisting of copper 1
and 2 skillings and a .500 fine silver 12 skilling.  Note
that the coins were struck with a lower intrinsic value than
homeland coins to encourage them to stay on the island.  The
12 skilling was supposed to serve as a Spanish real, but was
actually a bit underweight.  It has a ship design which
heightens its popularity, and is a rare sucker which turns
up infrequently in low grade.  The copper companions are
even rarer.
Two 12 skilling types were struck in 1748: with the
king's portrait and with his monogram.  Portraits are rarer,
but neither type shows up very often, and when they do
they're usually in "near slick" condition.  Single and
double ducats of 1749 are very rare once in a lifetime
auction items.
In 1754 the Company deeded the islands to the Danish
Crown government.  Royal paper money was issued starting in
1757, and though all types are extremely rare, 18th century
paper does show up from time to time.  Another 12 skilling
was issued in 1757, and in 1763 a 24 skilling was issued
supposedly equivalent to the Spanish 2 reales.  Being
bigger, and still bearing the ship reverse, they would be
very popular coins if only they would turn up in decent
condition.
The two denominations continued in issue through 1767,
when a 6 skilling was also struck.  The 6 is scarcer than
the other two types.  All of these show up very infrequently
in high grade and get prices in the high three to low four
figure range.  They're not at all common in poor-to-fair
either.
No coins were struck from 1767 to 1816.  There were
problems at home.  In the latter year a set of billon coins
of 2, 10, and 20 skillings were struck.  The 10 skillings
were intended to pass as a real, but were significantly
underweight.  All three denominations were continued in
various years until 1848.  Commonest of this series are the
1837 "flat top 3" 2 skilling, 10 skillings of 1845 and '47,
and 1845 20 skilling.  They're very tough in Uncirculated,
but turn up fairly frequently in VF or better.  You have to
look at them carefully though.  The climate in which they
operated tended to induce corrosion.
By 1849 Spanish money had just about disappeared and
the supply of skillings was totally inadequate.  The
government took to countermarking foreign coins.  The SCWC
listings show a rather polyglot set of host coins of
different sizes, weights, values.  No matter.  This series
is notorious for counterfeits.  It is a caveat emptor
situation with a vengeance.  One must be circumspect and
philosophical when purchasing these items, especially if the
host coin is from the USA.
Good enough.  Starting in 1859 a set of coins
denominated in cents was issued.  All the 19th century 1¢
coins are easy enough to find except for the 1879 date.  I
guess fine to very fine would be a normal grade range, with
corrosion a fairly common occurrence and uncirculated
basically unheard of.  The little 1859 3¢ is a bit tough,
usually found in low grade.  1859 5¢ is no problem in
circulated, '78 and '79 are a bit tougher.  Situation is
similar for the 10¢ and 20¢.
20th century issues start with the 1904-5 gold coins
which I've seen in auctions many more times than once, and
in uncirculated, not "AU" to boot.  Next come the 1905 coins
from ½¢ through 40¢, all of which can be found fairly
easily, though the "almost halfcrown" sized 40¢ with the
semi-nude ladies on reverse tends to go out of stock as soon
as it's offered.  1907 20¢ is not particularly common.  The
1913 1¢ does show up, but people always seem to want too
much for it, and it does look an awful lot like the cheaper
1905.  The 1913 40¢ is actually a rather tough coin.
I should mention that the only truly uncirculated DWI
coins I've seen was a 1767 12 skilling.