Which language has the best old literature?
I want to learn a language solely because I want to be introduced to a different culture, and I want to study old texts in their original language. Icelandic/Old Norse was my first choice but it's very hard and there are few resources. I did my best for a few months but I just couldn't find enough information. Then there's welsh, because of the King Arthur legends. I don't know many other languages except that. I'm looking for a really old language that can still be read today.
If you considered the amount of material available for Old Norse insufficient, then I suspect your choices largely boil down to Latin, ancient Greek, and modern standard Arabic, which is deliberately close to classical Arabic. And I would think ancient Greek is a good bit behind the other two in terms of available resources.
It's highly a matter of preference and personal perspective. I'm a native Farsi speaker, and I can say with certainty, that Persian literature is quite rich and diverse, and goes a long way back. I can also say that don't have the knowledge required to state which literature is "best" or "richest", if an absolute answer exists.
For dead languages, the ones with the most resources (and tons of texts, too) would probably be Latin and Ancient Greek. Depending on where you're from, Old Church Slavonic might also have a lot of available resources, although I admit I don't know what texts exist in that language, nor how high mutual intelligibility is with modern Slavic languages.
Hebrew makes an interesting middle case, as Ancient Hebrew should be very similar to Ancient Hebrew (never tried the latter myself, so I can't judge). Arabic has been mentioned above.
As for modern languages, the question of what remains understandable probably becomes a bigger question than the available literature. Most modern languages might enable you to understand texts written 600-800 years ago, but probably not much beyond that. If you learn Latin and the modern romance languages, that will probably enable you to read everything written in-between. Both Swedish and Norwegian should also work as a stepping stone towards Old Norse, if not as well as Icelandic.
For a few old texts I know about: If you like poetry, there's quite a bit of that in Middle French (François Villon is one of my favourites) and Middle High German (you might have heard of the Carmina Burana) and both can be understood decently well from the Modern languages. The italian Renaissance literature (Divine Comedy, Decamerone...) is also supposedly somewhat understandable from Modern Italian. You should probably read all of those in an annotated version, though.
Or go for really old and learn Middle or Late Egyptian ;) There's a fair amount of literature available in both of them.
"Icelandic/Old Norse was my first choice but it's very hard and there are few resources."
Fisrst, Icelandic and Old Norse are not the same nor is Icelandic the closest thing to Old Norse (that honor goes to Elfdalian). For one, the plural pronouns in Modern Icelandic are the dual pronouns in Old Norse, not to mention the differences in pronuncation. Second, there are a lot of Icelandic resources freely available on the internet if you know where to look. Resources for Old Norse are somwhat more difficult, but texts are easy enough to find.
If you want to learn Old Norse, try these:
http://www.heimskringla.no/wiki/Main_Page Things to read.