Ek kies kaas en eiers vir ontbyt.

This is the normal main-clause word order in Afrikaans:

• Ek = subject
• kies = verb
• kaas en eiers = what is being chosen
• vir ontbyt = prepositional phrase, for breakfast

So the pattern is basically:

Subject + verb + object + extra information

That is very similar to English: I choose cheese and eggs for breakfast.

Here is the job of each word:

• Ek = I
• kies = choose
• kaas = cheese
• en = and
• eiers = eggs
• vir = for
• ontbyt = breakfast

So:

• Ek kies = I choose
• kaas en eiers = cheese and eggs
• vir ontbyt = for breakfast

Because eiers is the plural form, meaning eggs.

• eier = egg
• eiers = eggs

In this sentence, the speaker is choosing more than one egg, or eggs in general, so the plural is used.

Afrikaans often leaves out an article when talking about things in a general way.

So:

• Ek kies kaas en eiers vir ontbyt = I choose cheese and eggs for breakfast

This sounds natural when you mean the foods in general, not a specific cheese or specific eggs.

If you wanted to be more specific, you could add other words, for example:

• die kaas = the cheese
• 'n eier = an egg

But in your sentence, the article is simply not needed.

Vir usually means for.

In this sentence, vir ontbyt means for breakfast.

So it tells you the purpose or meal context:

• Ek kies kaas en eiers vir ontbyt = I choose cheese and eggs for breakfast

This is very close to English usage.

Yes. Ontbyt can be used as:

• a noun: breakfast
• a verb: to have breakfast / eat breakfast

In your sentence, it is a noun after vir:

• vir ontbyt = for breakfast

Examples:

• Ontbyt is gereed. = Breakfast is ready.
• Ons ontbyt vroeg. = We have breakfast early.

A rough English-friendly guide:

• Ek ≈ ek with a short e like in bed
• kies ≈ sounds somewhat like kees
• kaas ≈ like kahs
• en ≈ like en in pen
• eiers ≈ roughly AY-ers or EI-ers
• vir ≈ often like fer or fur, depending on accent
• ontbyt ≈ roughly ONT-bait

A few helpful notes:

• aa in kaas is a long vowel.
• ei in eiers sounds like the ei/ay sound found in many Afrikaans words.
• y in ontbyt is not pronounced like English y in yes.

No. Kies is the general verb to choose.

You can use it for many things:

• Ek kies koffie. = I choose coffee.
• Sy kies 'n boek. = She chooses a book.
• Ons kies 'n datum. = We choose a date.

So in your sentence it just happens to be used with food.

Afrikaans verbs are much simpler than English verbs. In the present tense, the verb usually does not change much according to the subject.

So you get:

• Ek kies = I choose
• Jy kies = you choose
• Hy kies = he chooses
• Ons kies = we choose

Notice that Afrikaans does not add an English-style -s for he/she/it in the present tense.

That is one reason Afrikaans grammar often feels simpler to English speakers.

Yes, you may hear variations like that, especially if the speaker wants to emphasize for breakfast.

But the most straightforward, neutral version is:

Ek kies kaas en eiers vir ontbyt.

That order is natural and clear for learners.

Yes: it is simply a coordinated noun phrase, joined by en = and.

• kaas = cheese
• eiers = eggs
• kaas en eiers = cheese and eggs

Afrikaans uses en just like English uses and.

So this part is very simple structurally: noun + en + noun

No, not in the way German does.

One reason this sentence is learner-friendly is that the nouns stay simple:

• kaas
• eiers
• ontbyt

They do not change form because of gender or case. Afrikaans has largely lost that kind of system, so you do not need to worry about masculine/feminine/neuter noun classes here.