Εγώ προτιμώ ριγέ πουκάμισα για τη δουλειά, ενώ ο αδερφός μου αγοράζει μόνο καρό.

Yes. In Greek, the verb ending already shows the subject, so προτιμώ by itself can mean I prefer.
Εγώ is added for emphasis or contrast. Here it helps set up the comparison:

• Εγώ προτιμώ...
• ενώ ο αδερφός μου αγοράζει...

So the sense is something like I prefer..., whereas my brother...

προτιμώ is the 1st person singular present tense of προτιμώ: I prefer.

The ending -ώ is common in verbs of this type. In this sentence it describes a general preference, not something happening just right now.

ριγέ means striped. It describes the pattern of the shirts.

A useful thing for learners is that ριγέ is usually treated as an indeclinable adjective in Modern Greek. That means it often stays the same instead of changing form for gender, number, or case.

So you can get:

• ριγέ πουκάμισο = a striped shirt
• ριγέ πουκάμισα = striped shirts

The adjective ριγέ stays the same.

πουκάμισα is the plural of πουκάμισο (shirt). It is a neuter noun.

Here it is in the accusative plural, because it is the direct object of προτιμώ:

• προτιμώ πουκάμισα = I prefer shirts

For many neuter nouns, the nominative plural and accusative plural look the same, so πουκάμισα can serve both functions depending on the sentence.

Here για τη δουλειά means for work, in the sense of for wearing at work / suitable for work.

• για often means for
• τη δουλειά is the work/job in the accusative

So the phrase gives the purpose or context: these are the kinds of shirts the speaker prefers for work.

It does not mean movement to work. For that idea, Greek would usually use something else depending on the context.

Because για takes the accusative case.
The noun δουλειά is feminine, so:

• nominative: η δουλειά
• accusative: τη δουλειά

So after για, you use τη δουλειά.

Here ενώ means whereas or while, introducing a contrast.

It can sometimes mean:

• while in a time sense
• whereas / while in a contrastive sense

In this sentence it is clearly contrastive:

• I prefer striped shirts for work
• whereas my brother buys only plaid

So while is possible in English, but whereas shows the contrast more clearly.

In Greek, possessive pronouns like μου (my) usually come after the noun:

• ο αδερφός μου = my brother
• literally: the brother my

That is completely normal Greek word order.
So unlike English, Greek usually says the brother my, the car μου, the house μας, and so on.

Yes, αδερφός is correct and very common in everyday Modern Greek.

You may also see αδελφός, which is a more conservative or formal variant. In ordinary speech and writing, many Greeks use αδερφός.

So learners should recognize both:

• αδερφός
• αδελφός

They both mean brother.

Good question. Greek often leaves out a noun when it is obvious from the context.

Earlier, the sentence already mentioned πουκάμισα (shirts), so in the second half Greek can simply say:

• αγοράζει μόνο καρό

This means something like:

• he buys only plaid ones
• he buys only plaid shirts

Here καρό means checked / plaid, and the noun is understood.

καρό means checked, checkered, or plaid, depending on the context.

Like ριγέ, it is commonly used as an indeclinable pattern word, so it often stays the same form:

• καρό πουκάμισο
• καρό πουκάμισα

And in this sentence it appears by itself because πουκάμισα is understood from context.

μόνο means only, and here it focuses on the kind of pattern the brother buys:

• αγοράζει μόνο καρό = he buys only plaid

So the idea is not just that he only buys, but specifically that the only kind he buys is plaid.

Greek word order is flexible, but here μόνο καρό naturally groups together and emphasizes the restriction on the pattern.

αγοράζει is 3rd person singular present tense of αγοράζω: he/she buys.

It is present tense because the sentence is describing a habit or general preference, not a one-time event. Greek often uses the present for repeated actions:

• Εγώ προτιμώ...
• ο αδερφός μου αγοράζει...

So the meaning is about what each person generally does or prefers.