I've tried to have a look through /r/linguistics for you, here are some that might answer your question:

One Two Three

I can't find anything about Greek, sorry.

My Latin teacher in high school said that classical Latin would have been very nasally sounding, like French. Consonants were nearly always pronounced "hard".

For instance, the name Caesar would sound more like the German derivitave kaiser. The Romans did not use the letter W, and when the letter V appeared it was pronounced as we pronounce W in English. So, Caesar's famous quote, "Veni, Vidi, Vici" would have sounded phonetically: "we-ni, we-di, wi-ki". I'm not sure of the reasoning on why

On another important note, ecclesiastical Latin uses the fricative (normal English)pronunciation of the letter V, to explain what you hear when you go to church on Christmas and hymns like Adeste Fidelis (O come all ye faithful). It also palatalizes the consonant C before fronted vowels, so the above "vici" would, pronounced ecclesiastically would render phonetically as vi-chi)

Hope that helps to clear things up.

I studied Latin in school, therefore I'm just able to respond regarding Latin:

The way the language was spoken and pronounced changed a lot over the years, getting more and more different from the Latin which was spoken in the past. As there were not many hints on the original pronounciation left, scientists tried to reconstruct the basic rules the Romans followed, partially by texts from original Romans explaining their language or criticising flaws in it (even searching for misspellings works, as you often spell a word in the way it sounds to you if you do not know it better), the pronouncation of familiar words in ancient greek and the development of words in languages based on latin.

As you probably know, learning Latin helps you to learn other languages, for example king in latin is rex, whereas it is rey in spanish, roi in french and rei in portuguese...all spell nearly the same, guess italian is also close (dont speak it, so I can just guess), while German is different (König), but in other things it shares a lot.

Comparing how you spell those words nowadays hints at the original pronouncation, as it developed out of it