Modern Greek or Koine Greek can be used for pronouncing Ancient or Classical Greek. The problem found is that some Germanics and politically inclined individuals and groups have attempted to expand on their theories, for example the Dorian theory and hence the Germanic pronounciation. However, modern Greek represents in my opinion the closest in pronounciation. The Pontian and Cypriot dialects offer the best Ionian examples and with Macedonian or the Greek spoken in Thessaloniki you will have a definite ease in reading Plato. So as George mentions understanding the full picture helps. With that in mind: Modern Greek or any of the dialects I have provided are probably the first step towards understanding what was in the past.

Modern Greek pronunciation is new to me. Up till now I've been going by a half-Erasmian and half-made-up pronunciation scheme. So, I have a question: according to modern Greek pronunciation would eucharist be pronounced like ev-har-ist rather than hue-char-ist?

It is pronounced efharistia.

But Xristos would still be pronounced with a hard sound like Kristos? or would it be pronounced Hristos?

Hristos. X was never pronounced as a k.