Available in Upstate South Carolina
For several years I have taught my children Greek as part of their home-schooling. My method for this is following a standard approach to the language using either Machen’s “New Testament Greek for Beginners” or a popular modern home school curriculum.
Traditional instruction according to many courses involved a regular lesson on new grammar and vocabulary, after which followed a list of sentences to translate. This may be efficient for older students, but common home-schooling workbooks incorporate more basic exercises also, which is preferable to ensure that new concepts are well learned. Besides this, copying passages from the New Testament, and regular exercise with vocabulary flash-cards, are important elements of learning and retaining knowledge of the Greek language.
ευαγγελιον → Evangelion = Evangel = Gospel
For pronunciation my approach is to incorporate modern Greek pronunciation into lessons for Koine Greek. For example, rather than pronouncing β as Bay-ta, we will pronounce the letter as Vee-ta and sound its use according. Variants in the spelling of the name for David as either δαυιδ or δαβιδ evidence that some of the modern pronunciation is a better representation of Koine era pronunciation than what is found in other approaches.
At first, learning to pronounce new sounds will be foreign and difficult. This is not really different from learning a language like French. Other pronunciation approaches tend to avoid the difficulty in a way very artificial, tending to hide from students the real similarities and differences of sound for words spelled with different vowels, consonants, or diphthongs. One thing I can provide to help with the challenge is recordings of native Greek speakers reading the original New Testament scriptures. In the long run, familiarity with modern Greek pronunciation facilitates the potential of fluency and provides the sense that the student knows a real language which used to be spoken through a large part of the world.
If using the Greek Received Text, and KJV as a preferred English translation is important to you, I fully understand. That is my preferred approach, and while there is no concealing the fact that variants exist, I will encourage respect for the Received Text and KJV. I also admire the old Geneva translation of 1560. To accommodate the grammatical distinctions inherent in ancient Greek (as well as some modern languages too,) I always encourage English translations with a distinction of “thou” (singular 'you') and “ye” (plural 'you'). This is only found to be a challenge for the youngest students, but is still overcome quickly.