Learn Hardcore Japanese: watasi ha sigoto yori kazoku wo yuusen simasu.

The particle より marks the “than” part in a comparison. In the structure AよりBを優先する, you’re saying “I prioritize B over A.” Here, 仕事より means “over work,” and 家族を優先します means “(I) prioritize my family.”

Why is 私 marked with the topic particle は instead of the subject particle が?

Using 私は sets up “as for me” as the topic of the sentence—whose priorities we’re talking about. If you used 私が, it would emphasize “I” as the one doing the action, which isn’t wrong but feels less natural when stating a general preference.

Why is 家族 marked with を?

In AよりBを優先する, B is the direct object of 優先する (“to prioritize”). So 家族を優先します literally means “(I) prioritize my family,” and を marks 家族 as that object.

Can I drop 私は and just say 仕事より家族を優先します? Will it still be clear?

Yes. Japanese often omits the topic if it’s clear from context. 仕事より家族を優先します still means “I prioritize family over work.” The speaker (I) is understood.

What’s the difference between 優先します and 優先する?

優先します is the polite present form (masu-form) of 優先する, which is the plain (dictionary) form. Use 優先します in formal or polite contexts; 優先する in casual speech or writing.

How would I say this more casually?

You can switch to the plain form:
仕事より家族を優先する。
Dropping the polite ending makes it suitable for casual conversation.

Could I reorder the parts and say 家族を仕事より優先します?

Yes. Japanese word order is flexible as long as particles stay attached:

家族を仕事より優先します。

This still clearly means “I prioritize my family over work.”

Are there other verbs or expressions to convey the same idea?

Yes. You could say:

仕事より家族を大事にします。 (“I value my family more than work.”)
仕事より家族が大切です。 (“My family is more important than work.”)
Each uses different verbs/adjectives—大事にする (to value) or 大切だ (to be important).