ryokou no mae ni, huku wo suutukeesu ni tumete okimasu.

Both are possible, but they are built differently:

• 旅行の前に = before the trip
  • 旅行 is treated as a noun
  • の connects the noun to 前
• 旅行する前に = before traveling / before you travel
  • 旅行する is treated as a verb phrase

So:

• 旅行の前に、服をスーツケースに詰めておきます。 = Before the trip, I pack my clothes in my suitcase in advance.
• 旅行する前に、服をスーツケースに詰めておきます。 = Before traveling, I pack my clothes in my suitcase in advance.

The first one sounds a bit more like before the trip itself, while the second focuses more on before doing the action of traveling.

In 前に, the に marks a time point before which something happens.

So:

• 旅行の前に = before the trip
• literally, at the time before the trip

This pattern is very common:

• 食事の前に = before the meal
• 寝る前に = before going to sleep
• 出かける前に = before going out

With 前, you will very often see に when it means before X happens / at a time before X.

Because 旅行 is a noun, and when a noun modifies another noun in Japanese, you usually connect them with の.

Here:

• 旅行 = trip, travel
• 前 = front / before
• 旅行の前 = the time before the trip

This is the normal noun-linking pattern:

• 学校の前 = in front of the school
• 会議の前 = before the meeting
• 夏の前 = before summer

So の is simply connecting 旅行 and 前.

Because 服 is the direct object of 詰める.

• 服 = clothes
• 詰める = to pack / stuff / fill

So the thing being packed is 服, which is why it takes を:

• 服を詰める = to pack clothes

This is similar to:

• 本を読む = read a book
• 水を飲む = drink water
• 荷物をまとめる = organize/pack luggage

Here, に marks the destination/container that something is put into.

• スーツケースに詰める = pack into a suitcase

So the structure is:

• 服を = the thing being packed
• スーツケースに = into the suitcase
• 詰めておきます = pack in advance

This use of に is common when something goes into something:

• 箱に入れる = put into a box
• かばんに入れる = put into a bag
• 瓶に詰める = pack/fill into a bottle

In this sentence, 詰める means to pack things into a container, especially by fitting them in.

It can also mean things like:

• to fill
• to stuff
• to cram

In the context of travel, 服をスーツケースに詰める means to pack clothes into a suitcase.

Compared with 入れる:

• 入れる = put in
• 詰める = pack in / stuff in / fill in

So 詰める gives more of a packing luggage feeling than the more general 入れる.

〜ておきます is a very important pattern. Here it means:

• do something in advance
• do something beforehand, for preparation

So:

• 詰めます = pack
• 詰めておきます = pack in advance / pack beforehand

In this sentence, it implies preparation for the trip:

• 旅行の前に、服をスーツケースに詰めておきます。 = Before the trip, I pack my clothes in my suitcase in advance.

This pattern often has a practical, preparatory nuance:

• 予約しておきます = I’ll make a reservation in advance
• 買っておきます = I’ll buy it beforehand
• メモしておきます = I’ll make a note of it in advance

Not always. It has two main common uses:

1. Do something in advance / as preparation

   • 切符を買っておきます。
   • I’ll buy the ticket in advance.

2. Do something and leave it that way

   • 窓を開けておきます。
   • I’ll leave the window open.

In your sentence, the first meaning is the important one: packing in preparation for the trip.

おきます is the polite non-past form. In Japanese, the non-past can refer to:

• present
• future
• habitual actions

So here it can mean:

• I pack my clothes before a trip (habitual)
• I will pack my clothes before the trip (future)
• depending on context

Japanese does not need a separate future tense the way English does.

If you wanted to talk about a completed past action, you could say:

• 旅行の前に、服をスーツケースに詰めておきました。
• I packed my clothes in my suitcase beforehand.

When おく is used as part of the grammar pattern 〜ておく, it is very often written in hiragana:

• しておく
• 買っておく
• 詰めておく

This helps show that it is functioning as an auxiliary expression, not as the full verb 置く meaning to place.

So:

• 本を机に置きます = I place the book on the desk
• 準備しておきます = I prepare it in advance

Writing おく / おきます in hiragana is very common in this grammar usage.

Japanese nouns usually do not show singular/plural clearly unless the context makes it necessary.

So 服 can mean:

• a piece of clothing
• clothes
• clothing

In this sentence, English naturally translates it as clothes, because packing for a trip usually involves more than one item.

That does not mean the Japanese sentence must use a special plural form. Japanese often leaves number unstated.

It could be either, depending on context.

Because おきます is non-past, this sentence can mean:

• I pack my clothes in advance before a trip.
  → a habit / general practice
• I will pack my clothes in advance before the trip.
  → a future action

Japanese often relies on context to tell you which one is meant.

Yes. 荷物 means luggage / baggage / belongings, so it would make the sentence broader.

Compare:

• 服をスーツケースに詰めておきます。 = I pack my clothes into my suitcase in advance.
• 荷物をスーツケースに詰めておきます。 = I pack my luggage/belongings into my suitcase in advance.

Using 服 focuses specifically on the clothes. Using 荷物 includes other travel items too.

It is the most natural one in this sentence.

With verbs like 詰める and 入れる, に commonly marks the container or destination:

• かばんに入れる
• 箱に詰める
• スーツケースに詰める

You may sometimes see other particles in different sentence structures, but for pack X into Y, Y に is the standard choice here.