The one good thing about Greek compared to English is that, with very, very few exceptions, a particular letter combination always sounds the same. Once you have learnt them that's it. It is fairly easy to get to the point where you can read a Greek word and say it out loud more or less correctly.
To offset that the grammar is fiendishly complicated. The key advice is to learn every noun with the appropriate word for "the" in front of it. Altogether, logically, there are 18 words for "the" although some of them are identical and some that are not identical sound identical. If you ever get to the stage of trying to speak Greek correctly, and I haven't after 20 years, you are going to need to know the gender of every noun and many are anything but obvious. You will never remember them as an abstract concept, although you will learn to make an intelligent guess from the ending. Typically we learn nouns in the nominative case singular and the three words for "the" in that case are: ο, masculine, η, feminine and το, neuter. So don't learn father, mother, person as πατέρας, μιτέρα, άτομο, learn them as ο πατέρας, η μιτέρα and το άτομο. If they stick in your mind like that then later you won't need to wonder what is the gender, the word for "the" tells you. It's also good practise because Greek sticks "the" in front of nouns in many places where English doesn't such as names. For example if somebody was talking about me they would refer to me in English as "Warwick" but in Greek as "ο Γουορικ" or possibly "τον Γουορικ" or "του Γουορικ" depending on where I appeared in the sentence.
I am not sure what is a good book to start with but if you really want to learn the grammar "Greek - An Essential Grammar of the Modern Language"
is excellent but anything but easy and not cheap. I've got the earlier version
. "Essential Modern Greek Grammar"
would be a cheaper alternative but I don't have any experience of it. "201 Modern Greek verbs"
is also quite useful as it conjugates all 72 forms, plus about 9 variants, for the 201 verbs included in it.
PS Yes you did read that correctly. 72 forms plus about 9 variants. There are 11 tenses each of which has 6 forms, i.e. first, second and third person singular and plural plus 2 tenses that have 2 forms and 2 that have a single form. Then there are variant endings, especially on the first person plural.