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What a begginner should read?

Greek is not a very easy language to start with. Unless you are already familiar with the greek alphabet it may be better to try learning a few simple, oral everyday dialogue verses. It is easier to advance first with its sound and later proceed to reading.
Try to start speaking Greek with sincere and educated people who will not teach you unkind words or phrases. It is very intimidating to find out later that the few things you've learned from your friends are actually poor slang.

Greek has loud vowels, similar to Spanish and Italian and not a very complex variety of consonants. If you are a native Portuguese speaker adjusting to the sound of Greek will not be a hard task for you.

You could start learning the personal pronouns and their possessive cases in singular:

I εγώ
you εσύ
he/she αυτός/αυτή


as well as start learning the auxiliary verbs:

(I) am είμαι
(you) are είσαι
(he/she) is είναι

and soon start building small sentences with pronoun+aux. verb and adjective.

Είμαι χαρούμενος (I am happy) {i'me haro'umenos}
Eίσαι έτοιμή? (are you ready?) {'ise 'etimi ?}

I am sure Arialena will be happy to give you more advice on how to proceed.

http://www.italki.com/teacher/T007685295.htm
And me, I can always add some buzz and fun to your learning. It takes time.

Start slow. Learning a language is like saving money, little by little. And after some time you may look back and find you have truly worthy savings!