In terms of learning the language, most people start with the Attic of Demosthenes, Plato etc. There's a lot of material there, and it also became a prestigious literary language that later ages would look back to and emulate. Hence you get a lot of 'Atticising' literature, written much later but with similar vocabulary and grammar.
In terms of available texts to learn with, they are ample for Attic Greek. There's also a large amount of Ionic prose in the form of Herodotos' Histories, which are both long and varied in content.
The Greek Septuagint and New Testament alone provide ample Koine material.
Of course, there's also Homeric Greek, an artificial poetic dialect in which most hexameter is written. It's maybe not the best place to start though, as it is filled with different grammatical forms from different times and dialects, as well as some that are purely made up to fit the metre. The same might be said of the choral 'Doric' dialect of Pindar.
Another problem (if you're starting from scratch) is textbooks. I've never seen a textbook which starts with Ionic, for example. This is to some extent down to the historical priorities of the subject. People interested in Classical literature tend to start with Attic so they can read Plato, Demosthenes, Aristophanes, etc., whilst people interested in theology and reading the Bible in Greek tend to start with Koine for the Biblical material. Homer is also prestigious but for the reasons mentioned above no one really starts off with it. As for your chances of finding a textbook starting from scratch for, say, Pamphylian, they are pretty much zero.
To be honest, none of this is that much of a problem; the dialects don't differ an enormous amount, and once you know, say, Attic and the various sound changes which separate it from the other dialects, they are more or less comprehensible.
I bet that from the above time frame (600-100 BC) , most of them are from 100.
Not especially. There are plenty of texts from the 'Classical period' (Plato, for example, and the Attic orators); most Greek tragedy is 5th-4th century. And there's also a fair bit of Hellenistic literature, eg. Apollonius'
Argonautica. But not a lot from the second century.