At the start of his book Ghost on the Throne: The Death of Alexander the Great and the War for Crown and Empire (Alfred A. Knopf: 2011) [see: my review], Bard College Classics professor James Romm offers compact and comforting advice on pronouncing Greek names. He says:
"Readers should feel no fear in pronouncing proper names, since there are few ways they can go wrong. The evolution of the names from Greek to Latin to English means that there is often more than one valid way to sound them out.... Many classicists are eclectic, choosing whichever sounds right in a particular word.... C can be sounded soft, like s, or hard, like k."
Note: ch, as in Achilles, is pronounced as a k.
Romm adds that the -es at the ends of names is always pronounced -eez, that a terminal e is always pronounced, there are no silent letters [if you want to worry about the h in the English orthography, you can aspirate the k-sound when you pronounce Achilles], and in most four-syllable names, the stress is on the second syllable. Romm, who also edited the Landmark Edition - Arrian's The Campaigns of Alexander, provides a common exception to this rule, the name Alexander, which is stressed on the third syllable.
Note: in a two-syllable word, stress the first, just as you would in the familiar Greek restaurant exclamation, Opa! In a word of three syllables, it gets more complicated. You stress the second or the first, depending on length of the second syllable. For the word Achilles, for instance, most people I've heard stress the middle syllable as Uh-'kil-eez, but 'Ah-kil-lace or 'Ah-kil-eez would be recognizable pronunciations.