You might try your hand at Latin first and see if you can handle it. It’s good for being able to read a vast number of church documents, Biblical commentary, historic documents, etc, in the original, but has the benefit of using the Roman alphabet. The thing to remember about Latin is that there is no word order, so the ending of the word changes depending on the part of speech it’s used as— just like you conjugate your verbs (I walk, you walk, he/she/it walks, we walk, they walk, plus all the other tenses), you also decline your nouns, so the word ending changes depending on whether it’s being used as the subject, a direct object, an indirect object, etc. An adjective, for example, might have 90 different possible endings, depending on whether it’s modifying a masculine, feminine, or neuter noun; whether that noun is singular or plural, and the part of speech that noun currently occupies. So you don’t have a “blue” something; you have something far more specific.
With Greek, I believe you have many common linguistic rules, but you have the added difficulty of having to sit down and learn to work with a whole new alphabet. I don’t know for sure, because Latin ate my lunch before I ever got to Greek.

I definitely have a vast admiration for people who can work fluently and beautifully in a foreign language.
So I think both Latin and Greek are useful when it comes to Biblical studies, but unless you’re planning on reading a lot of church documents from the Eastern rites, like wanting to read the
Philokalia in the original, you might try starting with Latin and delving deeper into Greek afterwards.