Learn Hardcore Japanese: kaigairyokou ha takai desu kara, okane ga hituyou desu. - Overseas travel is expensive, so money is necessary.

は is the topic marker, setting “overseas travel” as the topic of the sentence. It tells the listener, “As for overseas travel…,” and then describes it. If you used が, you’d be marking a new subject or emphasizing it; here we simply want to introduce the topic.

Why is です attached to 高い?

高い is an i-adjective. In polite speech, you add です after adjectives (both i- and na-adjectives) to soften and make them more courteous: 高いです. In casual speech you can drop です and just say 高い.

Why does から follow 高いです instead of 高い in the plain form?

While the plain form works (高いから), Japanese allows you to attach から to the polite form (高いですから) if you want to keep the whole sentence polite. Both 高いから and 高いですから mean “because it’s expensive,” but the latter matches a polite register.

What’s the difference between から and ので for giving a reason?

から is a straightforward “because” and can sound a bit more direct.
ので is softer and often more formal or explanatory.
Usually you use the plain form before ので (e.g. 高いので), whereas から can be attached to plain or polite forms.

Why is が used after お金 instead of を?

In the pattern Xが必要です, 必要 is a な-adjective meaning “necessary,” and X is what is necessary. が marks the thing that exists or is needed. を marks the direct object of an action verb, but here 必要 isn’t a verb, so we use が.

What part of speech is 必要 and how does it behave?

必要 is a な-adjective (sometimes called a nominal adjective).

As a predicate: 必要です
To modify a noun: 必要なもの (“necessary thing”)

Could I say お金が要る instead of お金が必要です? What’s the nuance?

Yes. 要る (いる) is a verb meaning “to need.”

お金が要る is more direct and casual.
お金が必要だ/です is a little more formal or neutral because 必要 is a na-adjective.

How would I say this sentence in casual speech?

Drop the polite copula です and use plain forms:
海外旅行は高いからお金が必要だ。
In very casual speech you can even drop the final だ:
海外旅行は高いからお金が必要。