Карьерный рост для меня важен.

Важен is the short form of the adjective важный.

In Russian, short-form adjectives are often used:

• as the main predicate of the sentence
• especially in statements like X is important / necessary / useful / ready, etc.

So:

• Карьерный рост важен. = Career growth is important.
• Карьерный рост важный. sounds unnatural here.

A full adjective like важный is usually used before a noun:

• важный вопрос = an important question

Since рост is masculine singular, the short form is:

• masculine: важен
• feminine: важна
• neuter: важно
• plural: важны

Because it is the grammatical subject of the sentence.

The sentence is built like this:

• Карьерный рост = the thing being talked about
• важен = is important
• для меня = for me

So карьерный рост stays in the nominative, because it is the subject.

You can think of the structure as:

• [Subject] + [short-form adjective] + [for whom]

Because карьерный agrees with рост.

The noun рост is:

• masculine
• singular
• nominative

So the adjective must also be:

• masculine
• singular
• nominative

That gives:

• карьерный рост

Compare:

• карьерная цель = a career goal
• карьерное развитие = career development
• карьерные планы = career plans

Для меня means for me or to me, personally in the sense of viewpoint or importance.

It shows whose perspective the statement is about:

• Карьерный рост для меня важен. = Career growth is important to me / for me.

Grammatically:

• для requires the genitive case
• я becomes меня

So:

• для меня = for me
• для него = for him
• для нас = for us

Yes, absolutely. That is also correct and very natural.

Both mean roughly the same thing:

• Карьерный рост для меня важен.
• Мне важен карьерный рост.

The difference is mostly about style and emphasis.

Мне важен карьерный рост

This is often a bit more direct and compact. It is a very common Russian way to say that something matters to someone.

Карьерный рост для меня важен

This can sound slightly more emphatic or contrastive, as if you are highlighting for me personally.

For example:

• Для кого-то важна стабильность, а для меня важен карьерный рост. = For some people stability is important, but for me career growth is important.

So both are good; the version with для меня often feels a bit more explicitly contrastive or personal.

Because in Russian, the verb to be is usually omitted in the present tense.

So Russian says:

• Карьерный рост для меня важен.

But in English we need:

• Career growth is important to me.

In the past or future, forms of быть appear:

• Карьерный рост был для меня важен. = Career growth was important to me.

• Карьерный рост будет для меня важен. = Career growth will be important to me.

Yes. Russian word order is flexible, and changing it usually changes emphasis, not the basic meaning.

Possible versions include:

• Карьерный рост для меня важен.
• Для меня карьерный рост важен.
• Карьерный рост важен для меня.
• Мне важен карьерный рост.

All are possible, but they do not sound identical in focus.

Common nuance:

• Карьерный рост для меня важен
  neutral, with some focus on the whole statement

• Для меня карьерный рост важен
  stronger emphasis on for me

• Карьерный рост важен для меня
  often puts extra emphasis at the end on for me

• Мне важен карьерный рост
  very natural, compact, common in speech

It is a very common collocation, yes.

Карьерный рост is a standard Russian expression for:

• career growth
• career advancement
• moving upward professionally

It is widely used in:

• job interviews
• business contexts
• CV/resume language
• workplace discussions

Other related expressions include:

• профессиональный рост = professional growth
• развитие карьеры = career development
• продвижение по карьерной лестнице = moving up the career ladder

So карьерный рост is very normal and idiomatic.

Because важен agrees with рост, which is a masculine singular noun.

Russian short-form adjectives agree in gender and number:

• рост важен — masculine singular
• карьера важна — feminine singular
• развитие важно — neuter singular
• перспективы важны — plural

Важно would be correct in sentences where the subject is neuter, or where Russian uses an impersonal construction, for example:

• Мне важно работать в хорошей команде. = It is important for me to work in a good team.

But here the subject is the noun рост, so we need важен.

Yes.

Карьерный рост для меня важен / Мне важен карьерный рост

These mean:

• Career growth is important to me

The noun карьерный рост is the thing being described as important.

Мне важно + infinitive / clause

This often means:

• It is important for me to...

For example:

• Мне важно развиваться. = It is important for me to develop.
• Мне важно, чтобы работа была интересной. = It is important for me that the job be interesting.

So:

• Мне важен карьерный рост = a noun is important to me
• Мне важно расти в карьере = it is important for me to grow in my career

Both are natural, but the grammar is different.

The main stresses are:

• карьЕрный
• рост
• для менЯ
• важЕн

A simple stress-marked version is:

карьЕрный рост для менЯ важЕн

A rough pronunciation guide:

• карьерный ≈ kar-YER-nyy
• рост ≈ rost
• для меня ≈ dlya mi-NYA
• важен ≈ VA-zhen

A more natural spoken rhythm is:

• карьЕрный рост для менЯ важЕн

It sounds mostly neutral and quite natural.

It would fit well in contexts like:

• a job interview
• talking about career goals
• discussing priorities at work
• writing about professional values

It is not slangy, and it is not overly bookish either.

If you wanted a more conversational version, you might hear:

• Мне важен карьерный рост.

If you wanted a more elaborate or formal version:

• Для меня карьерный рост имеет большое значение. = Career growth is very important to me / has great significance for me.

So the original sentence is standard, clear, and neutral.