I think modern Greek and ancient Greek are not that different from each other. I was able to read an article in modern Greek based on my Koine comprehension. Grammar seems to be the main difference, Koine has archaic grammar. Modern Greek also has some modern vocabulary.
I have a high level in Arabic, and based on what little Syriac I have come in contact with, it's similar to Arabic, grammatical and vocabulary wise. Any Syriac/Arabic speaker can correct me if I am wrong.
Learning any language takes time, but it is certainly helpful to have knowledge of a similar language when learning the target language. Arabic helps me a lot with Hebrew, for example.
If you want to know how long it will take, it depends on what level you want to achieve. If you want absolute fluency, it might take a lifetime.
I can read articles and subtitles in Spanish almost perfectly. I started learning Spanish in 2010, so if you're dedicated it could take around that long. Spanish is close to English, vocab wise, so that might give you an idea.