Το βασικό μου κίνητρο για τα ελληνικά είναι να μιλάω πιο άνετα στην Ελλάδα.

Because κίνητρο is a neuter singular noun, so the article and adjective have to match it:

• το κίνητρο = the motivation
• το βασικό κίνητρο = the main/basic motivation

Greek adjectives agree with the noun in gender, number, and case, so:

• ο βασικός λόγος
• η βασική ιδέα
• το βασικό κίνητρο

Here, βασικό is the neuter singular form.

μου means my.

In Greek, possessive words like μου, σου, του, της are usually weak pronouns that often come after the noun or adjective phrase, not before like English my.

So:

• το βασικό μου κίνητρο = my main motivation

This word order is very normal in Greek.

You may also see other patterns, such as:

• το κίνητρό μου = my motivation

So Greek does not copy the English structure my + noun directly.

Here για means something like for, regarding, or when it comes to.

So:

• το βασικό μου κίνητρο για τα ελληνικά
  = my main motivation for Greek / for learning Greek

It does not mean physical direction here. It introduces the area or subject the motivation is connected to.

Similar uses:

• ενδιαφέρον για τη μουσική = interest in music
• αγάπη για τις γλώσσες = love for languages

Yes, it refers to one language, but Greek commonly names languages with a neuter plural form:

• τα ελληνικά = Greek
• τα αγγλικά = English
• τα γαλλικά = French
• τα ισπανικά = Spanish

So even though it looks plural, it is the normal way to refer to the language.

This is something English speakers just have to get used to: the grammar looks plural, but the meaning is simply the Greek language.

Because they are doing different jobs:

• Ελλάδα is a proper noun: the country Greece
• ελληνικά is the name of the language, written in lowercase in normal Greek spelling

So:

• στην Ελλάδα = in Greece
• τα ελληνικά = Greek

This is similar to how some languages treat language names differently from country names.

Greek often uses να + verb where English uses an infinitive like to speak.

Since Modern Greek does not have an infinitive in the same way English does, it uses να plus a verb form instead.

So:

• είναι να μιλάω πιο άνετα
  literally something like is to speak more comfortably

In this sentence, να μιλάω expresses the content of the motivation: what the motivation is about.

So the structure is very natural Greek, even if it feels different from English.

This is about aspect.

• μιλάω = imperfective aspect
  suggests an ongoing activity, general ability, or repeated action
• μιλήσω = perfective aspect
  suggests a single complete act or event

Here the idea is speaking more comfortably in general, not just managing to speak once. So μιλάω fits better.

Compare:

• Θέλω να μιλάω καλύτερα ελληνικά.
  = I want to speak Greek better, generally
• Θέλω να μιλήσω μαζί του αύριο.
  = I want to speak with him tomorrow, on a specific occasion

Because it modifies the verb μιλάω, not a noun.

• άνετος / άνετη / άνετο = comfortable, relaxed
• άνετα = comfortably / with ease

So:

• μιλάω πιο άνετα = I speak more comfortably

If you used άνετος, you would be describing a person, not the way the speaking happens:

• Είμαι άνετος = I am comfortable / at ease

But here the sentence means to speak more comfortably, so the adverbial form άνετα is right.

στην is a contraction of:

• σε
  • την = στην

So:

• στην Ελλάδα = in Greece

The preposition σε can mean in, at, or to, depending on context. Here, with μιλάω πιο άνετα στην Ελλάδα, it means in Greece.

Examples:

• μένω στην Ελλάδα = I live in Greece
• πάω στην Ελλάδα = I’m going to Greece

So the exact English translation depends on the verb and the context.

In Greek, country names are very often used with the definite article, especially after prepositions.

So Greek normally says:

• στην Ελλάδα
• στη Γαλλία
• στην Ιταλία

not usually bare forms like English in Greece, in France, etc.

This is a common difference between Greek and English: Greek uses articles more often with place names.

Yes. Greek word order is more flexible than English.

All of these are possible, with slightly different rhythm or emphasis:

• Το βασικό μου κίνητρο...
• Το βασικό κίνητρό μου...
• Κίνητρό μου είναι... (in a different structure)

Your original sentence is natural and clear.

A useful thing to notice is that when μου comes after a noun like κίνητρο, the noun may get an extra written accent:

• το κίνητρο
• το κίνητρό μου

That is a spelling feature connected with enclitic pronouns like μου.

Yes, Greek allows some movement here.

These are all possible, though the nuance or emphasis may shift a little:

• να μιλάω πιο άνετα στην Ελλάδα
• να μιλάω ελληνικά πιο άνετα στην Ελλάδα
• να μιλάω πιο άνετα ελληνικά is less natural

In your sentence, πιο άνετα comes right after μιλάω, which is a very natural place because it directly modifies the action of speaking.

So the original wording sounds smooth and idiomatic.

In this sentence, main is the better natural English equivalent.

Although βασικός can sometimes mean basic, it often also means:

• main
• principal
• key

So:

• Το βασικό μου κίνητρο...
  is most naturally understood as
  My main motivation...

That is probably the sense intended here.