Has anyone studied Ancient Greek?
My additional major as an undergrad was classical languages. I studied other ancient languages (and of course German, French, and Italian), but of all the languages I spent time on as electives or for the classical languages major, I spent the most on ancient Greek. I did my senior thesis on a cognitive and typological analyses of the Attic Greek impersonal constructions, and even had a minor paper on Euripides' Medea published.
Not particularly. Of course, "hard" is entirely relative in a number of ways. Some people have more difficulty with languages than others, some people absorb languages like sponges when they can be immersed in the language & culture (or approximately so), but this isn't an option for dead languages (even language classical language immersion programs aren't the same as there are no native speakers and no native speech communities). Also, and perhaps most importantly, there is difficulty learning a particular language given the language(s) you already know, particularly the language or languages you are a native speaker of. Greek is Indo-European, and thus has some familiar structures even to English speakers for whom the Germanic declensions and Latin-based verbal inflexions are almost entirely alien. The alphabet is relatively easy to learn. In contrast, neither Hebrew nor Arabic have alphabets that contain vowels other than aleph, Arabic in particular is difficult here due to the ways in which the letters are formed when they appear in different locations in words, and the grammatical structures are often wholly alien (e.g., the grammatical gender of verbs, which are indexed in lexicons by the 3rd person masculine form, typically) as is much construal of abstract (grammatical/syntactic) linguistic properties such as Tense-Aspect-Modality.
For a native Arabic speaker, however, Biblical Hebrew and Syriac is vastly easier than is Attic Greek.
I would also recommend standard classical Greek courses even if you are more interested in Greek of the Hellenistic era or e.g., Homeric Greek, as it is easy to go from learning Attic and Ionic Greek to reading the koine of the New Testament (for example), while the reverse is not true.
Are there any particular basic texts that are usually looked at during such courses?
The standard reference texts in English are (for Grammar) Smyth-Messing's
Greek Grammar and (for lexicons) the LSJ for ancient Greek generally and the BDAG for NT early Christian literature (as well as the more general Koine of the period).
These aren't particularly great for learning though. I would highly recommend the
Athenaze textbooks, which are modern in approach and have you reading (vastly simplified) ancient Greek from the start, rather than translating obscure lines as the only exposure to reading Greek early on while most of your time is spent memorizing grammatical rules and vocab. Couple this with a few readers (like Morrice's
Stories in Attic Greek) as well as some of the material provided by the Joint Association of Classical Teachers (e.g.,
An Independent Study Guide to Reading Greek,
Reading Greek: Text and Vocabulary, etc.) and that should take you well into intermediate levels where you can start reading entire texts in Greek that are designed for Greek learners with grammatical/translation guides and lexical aids in the text, such as
Plato: A Transitional Reader by Willie Major or
Plato: Apology: Text, Grammatical Commentary, Vocabulary by James J. Helm).
