The problem is that the ancient and modern Greek alphabets are slightly different. The ancient pronunciations map more easily on to our alphabet. I find the modern ones less intuitive e.g. beta being a V sound. There is an example below, where someone writes Bravo in modern Greek, and uses "mu beta" for the "b" sound and "beta" for the "v" sound.
As a fun fact, both Cyrillic letters Б б sounding "b" and В в sounding "v" were historically derived from Greek Β β.
B/V shifts or mergers are very common, notably in many Spanish variants they will, for example, write “vaca”, betraying the latin root “vacca”, but very clearly say “baca”. Coming from a language that clearly differentates between these sounds, it’s surprising how close they are.
For ancient Greek, two great books are:
Greek: an Intensive Course by Hansen and Quinn.
Basics of Biblical Greek by William Mounce
Both are standard texts with solutions easily available online.