amagu to undougutu wo zyunbisuru.

と connects nouns and means and in this sentence.

So:

• 雨具と運動靴 = rain gear and athletic shoes

Here, と gives a complete list of the items being mentioned. It sounds like these are the things to prepare.

Because 雨具と運動靴 is one combined object phrase.

The structure is:

• [雨具と運動靴] を 準備する

So both nouns together are the thing being prepared. In English, it works the same way:

• Prepare rain gear and athletic shoes.

You do not need a separate を after each noun.

を marks the direct object of the verb.

The verb is 準備する, and the thing being prepared is:

• 雨具と運動靴

So を shows what the action is being done to.

A simple way to think of it:

• X を 準備する = prepare X

They are read:

• 雨具 → あまぐ
• 運動靴 → うんどうぐつ

A few notes:

• 雨 = rain
• 具 = equipment / gear
• so 雨具 means rain gear or rain equipment

And:

• 運動 = exercise / sports
• 靴 = shoes
• so 運動靴 means athletic shoes, sneakers, gym shoes, etc.

The dictionary form is often used in:

• written instructions
• lists
• notices
• headings
• manual-style language

So 雨具と運動靴を準備する。 can sound like an instruction such as Prepare rain gear and athletic shoes.

If you wanted to make it more polite in conversation, you could say:

• 雨具と運動靴を準備します。
• 雨具と運動靴を準備してください。

The dictionary form is not automatically rude; it often just sounds neutral and instructional.

No subject is stated, but Japanese often leaves the subject out when it is obvious from context.

Depending on the situation, the unstated subject could be:

• you
• we
• participants
• parents
• students

So the sentence can work as a general instruction without saying exactly who must do it.

Both are possible.

• 雨具と運動靴を準備する
• 雨具と運動靴の準備をする

But they are not exactly the same in structure.

1. X を 準備する

This directly means prepare X.

• 雨具と運動靴を準備する
• Prepare rain gear and athletic shoes.

2. X の準備をする

This means do the preparation for X.

• 雨具と運動靴の準備をする
• Do the preparation for rain gear and athletic shoes.

In your sentence, 雨具と運動靴を準備する is very natural and straightforward.

Yes, but the nuance changes.

• と = an explicit, complete list
• や = such as, an incomplete list

So:

• 雨具と運動靴を準備する

  • Prepare rain gear and athletic shoes.
  • These are the named items.

• 雨具や運動靴を準備する

  • Prepare things such as rain gear and athletic shoes.
  • These are examples, not necessarily the full list.

In your sentence, と is better if those are the specific required items.

No, normally Japanese is written without spaces.

A natural written version is:

• 雨具と運動靴を準備する。

Spaces are often added in beginner materials to make the structure easier to see. They help learners notice:

• the nouns
• the particles
• the verb

But in real Japanese writing, you usually would not see those spaces.

Yes.

• 靴 = shoes in general
• 運動靴 = athletic shoes / sneakers / gym shoes

So 運動靴 tells you the type of footwear more clearly. It suggests shoes suitable for physical activity, not just any shoes.

That is why it is useful in instructions for school events, trips, or sports-related activities.