Again, sorry if this is a double post (something goofy is going on
with the posts, since I posted the last one twice and it only showed
up on the second try). Almost completely right (to the other two
replies), but please let me add that if you want to learn the most
valuable living Scandinavian language, learn Swedish. Technically,
they make a differentiation between Nordic (Finnish and Icelandic plus
the Scandinavian countries) and Scandinavian (Sweden, Denmark,
Norway), so Icelandic is Nordic, but I always refer to it as
Scandinavian. Finnish is the oddball, though they are close friends of
Scandinavians in the sense that they have a lot in common and share a
friendly border and geographic proximity to Scandinavians. Modern
Icelandic is a wonderful language, and its morphology, grammar, and
syntax has remained almost entirely in tact from the form people learn
when they study Old Norse, i.e. "classical" Icelandic. The reason I
recommend Swedish, is that, although lacking in most grammatical
remnants of Old Norse (the extent is not as much as many people claim
though), it's vocabulary is largely intact and its accentuation and
intonation is very conservative, more so than Bokmål Norwegian and
Danish. Nynorsk is somewhere about 3/4 to Bokmål from Old Norse, but
definitely preferable if you want to be able to speak to about three
times the amount of people as those from Iceland (it is an official
language of Norway, but it represents only about 13% of Norwegians).
Swedish, on the other hand, has only one significant dialect (at least
in the sense that it may be transferred with no significant difficulty
to every living dialect in Sweden and Finland). German is a good
option as well, since it is a little less difficult than Icelandic
grammatically, and it is spoken by the largest amount of speakers in
the whole of Germanic languages (excluding, of course, our own
language, English). German is also West Germanic, and if you learn the
2nd sound shift and take a formal course, you can learn it with just a
little work. German is also offered at many high schools, community
colleges, community centers (German-related institutes), universities,
and so forth. Plus, most of the American "Caucasian" (that means white
people, if you're dense) is of German-descent (meaning we all have a
little Kraut in us, more or less). French is an important romance
language, but will get you nowhere with Germanic languages, Spanish
just as little (despite some significant amount of nouns from Germanic
Visigoths). Latin will teach you grammar, but if that is all you want,
why not German instead? Faroese is wonderful for philologists and
Scandinavists, but even less people speak it than Icelandic, and it is
only a bit more conservative than Nynorsk. Modern Icelandic is still,
by an insanely large degree, the closest living descendant of Old
Norse. Take this word, for a random example, in Old Norwegian:
'sjónhverfing' - "optical illusion," has change in Modern Icelandicto
'sjónkverfing.' The only change in pronunciation is that the initial
sj- has changed from s- and j- (pronounced like English 'y' in yes) to
Danish and Norwegian sj- pronounced like English 'sh.' And the other
change, h to k is noted in the spelling. There are numerous examples,
but if you can read and write Modern Icelandic, you would have the
greatest advantage available to read an older form of a Germanic
language in the North Germanic branch. Think of it as Old Icelandic (a
dialect of West Norse, Eastern Norwegian) with Danish pronunciation.
Lastly, although I love the Danes, Danish culture, the country of
Denmark, their language is ridiculously terrible sounding and hard to
understand when spoken. http://www.youtube.com/watch?v=s-mOy8VUEBk
Swedish is still the best option to learn as a modern Scandinavian
language. In relatively little time, a moderate level of mutual
comprehension can be obtained for the other two, Norwegian [easier]
and Danish [easy to read, almost impossible to understand]).

So in summary, the best three options are: 1) Modern Icelandic, 2)
Swedish 3) German. Although I'm sure a few people will debate the
positions of 2 and 3, if you want to get closer to Old Norse, that is
the best recommendation; that, or learn Old Norse and leave it as a
dead language you can only read and poorly pronounce and reproduce
(like in shows on the history channel).

If you're taking language courses this summer, it's unlikely they'll
have anything worth wasting money on. Save it until they offer German
or Old English.