Jeg køber ikke den der, for jeg vil hellere have den her.

In a normal main clause, Danish usually puts the finite verb in second position, and ikke comes after that verb.

So the pattern is often:

subject + finite verb + ikke + ...

Here:

• Jeg = subject
• køber = finite verb
• ikke = not

So: Jeg køber ikke den der = I’m not buying that one

This is very typical Danish word order. English often puts not differently, but in Danish, ikke usually comes after the conjugated verb in main clauses.

Compare:

• Jeg spiser ikke kød. = I do not eat meat.
• Han kommer ikke i dag. = He is not coming today.

Den der means that one or more literally that there.

It is used to point to something that is farther away from the speaker, or simply something contrasted with another item.

In this sentence:

• den der = that one
• den her = this one

So the speaker is contrasting two things:

• I’m not buying that one
• I’d rather have this one

A useful way to remember it:

• her = here = this
• der = there = that

Danish nouns have grammatical gender, and the pronoun must match the gender of the thing being referred to.

• den is used for common gender nouns
• det is used for neuter nouns

So if the item being talked about is a common-gender noun, you say:

• den her
• den der

If it were a neuter noun, you would say:

• det her
• det der

Examples:

• en stol → den her stol / den der
• et hus → det her hus / det der

So in your sentence, the hidden noun is presumably a common-gender noun.

That is the normal Danish way to form expressions like this one and that one.

Danish often builds them as:

• den her = this one
• den der = that one
• det her = this one (for neuter)
• det der = that one (for neuter)

English uses one word, like this or that, but Danish often uses a pronoun plus her/der.

You can also use them before a noun:

• den her bog = this book
• den der bil = that car

So the structure is very common and natural.

Hellere means rather or preferably.

In this sentence: jeg vil hellere have den her means I’d rather have this one

It expresses preference between options.

Common patterns:

• Jeg vil hellere blive hjemme. = I would rather stay home.
• Hun drikker hellere te end kaffe. = She prefers tea rather than coffee.

A very important related form is:

• gerne = gladly / like to
• hellere = rather
• helst = preferably / most gladly

So:

• Jeg vil gerne have den. = I would like that.
• Jeg vil hellere have den her. = I would rather have this one.
• Jeg vil helst have den her. = I would prefer this one most of all.

That is a very common Danish pattern.

Vil have often means want in natural English.

So:

• jeg vil have den literally looks like I will have it
• but in ordinary meaning it is often I want it

In your sentence: jeg vil hellere have den her is most naturally understood as I’d rather have this one

So even though have literally means have, the whole expression vil have often corresponds to English want.

Here for means because, not the English preposition for.

So: Jeg køber ikke den der, for jeg vil hellere have den her. = I’m not buying that one, because I’d rather have this one.

This is a coordinating conjunction, similar to one use of for in somewhat formal English:

• I stayed home, for I was tired.

In modern English, that sounds literary or old-fashioned, but in Danish for is completely normal in this meaning.

Because for is a coordinating conjunction, and after a coordinating conjunction Danish normally keeps normal main-clause word order.

So you get:

• for jeg vil ...
• men jeg vil ...
• og jeg vil ...

The subject stays before the verb:

• jeg vil

This is different from some subordinating conjunctions, where Danish word order changes.

For example:

• Jeg bliver hjemme, fordi jeg er træt.
  Here fordi introduces a subordinate clause.

But with for, the clause behaves like a main clause:

• ..., for jeg vil hellere have den her.

Both can often be translated as because, but they do not behave exactly the same.

• for is a coordinating conjunction
• fordi is a subordinating conjunction

In everyday learning terms:

• for links two main-clause-type ideas
• fordi introduces a subordinate clause

Your sentence with for:

• Jeg køber ikke den der, for jeg vil hellere have den her.

A version with fordi would also be possible:

• Jeg køber ikke den der, fordi jeg hellere vil have den her.

Notice that with fordi, the placement of words can differ, and learners often meet forms like:

• fordi jeg hellere vil have den her

So both can work, but for gives you straightforward main-clause word order after it.

In a simple main clause, the finite verb usually stays in second position. Here the finite verb is vil.

So:

• jeg = first element
• vil = second element
• hellere comes after the finite verb

That gives: jeg vil hellere have den her

This follows standard Danish V2 word order.

A subordinate clause can look different:

• ..., fordi jeg hellere vil have den her

So the position of hellere depends partly on clause type.

In speech, people sometimes leave out the connector and rely on pause and intonation, but in standard written Danish it is better to connect the clauses.

So the version with for is clearer and more natural in writing:

• Jeg køber ikke den der, for jeg vil hellere have den her.

You could also use:

• ..., fordi jeg hellere vil have den her.
• ..., men jeg vil hellere have den her.

The choice changes the nuance a little:

• for / fordi = gives a reason
• men = emphasizes contrast

Yes, very natural.

Danish speakers use these all the time when pointing out or contrasting objects:

• Jeg tager den her. = I’ll take this one.
• Ikke den der. = Not that one.
• Kan du lide den her eller den der? = Do you like this one or that one?

They are basic, everyday expressions and very useful to learn early.

Yes. If the noun is important, Danish can include it:

• Jeg køber ikke den der jakke, for jeg vil hellere have den her jakke.

But if the object is obvious from context, Danish often drops the noun and just says:

• den der
• den her

That sounds natural and avoids repetition.

So your sentence is a very normal, idiomatic way to speak when the speaker is pointing at two visible options.