Вместо того чтобы сразу покупать книгу, я сначала люблю полистать её и посмотреть оглавление.

Вместо того чтобы means instead of doing or more literally instead of the fact that one would do.

It is a fixed Russian construction:

• вместо = instead of
• того = of that
• чтобы = so that / to / that

In modern Russian, you usually just learn it as one chunk: вместо того чтобы + infinitive.

Examples:

• Вместо того чтобы работать, он спит. = Instead of working, he sleeps.
• Вместо того чтобы спорить, давай проверим. = Instead of arguing, let’s check.

In your sentence:

• Вместо того чтобы сразу покупать книгу...
  = Instead of buying a book right away...

So after this expression, Russian normally uses an infinitive, not a noun.

The comma is needed because вместо того чтобы сразу покупать книгу is an introductory subordinate construction before the main clause.

Structure:

• subordinate part: Вместо того чтобы сразу покупать книгу
• main clause: я сначала люблю полистать её и посмотреть оглавление

Russian generally separates this kind of clause with a comma:

• Вместо того чтобы молчать, он заговорил.
• Вместо того чтобы идти домой, мы остались.

So the comma is not optional here.

Покупать is the imperfective infinitive, and it fits well here because the sentence is talking about the action in a general sense, not one completed purchase.

Compare:

• покупать = to buy, as a process / in general / habitually
• купить = to buy and complete the purchase

In вместо того чтобы + infinitive, Russian often uses the imperfective when speaking about what one would normally do or about the action as an activity:

• Вместо того чтобы читать, он играет.
• Вместо того чтобы покупать книгу...

Using купить would sound more like instead of actually buying the book (as a completed act). That is possible in some contexts, but here the idea is broader: instead of immediately going into buying mode.

So покупать sounds more natural.

They are related, but they mean different things.

• сразу = immediately, right away
• сначала = first, at first, before anything else

In the sentence:

• сразу покупать = buy immediately / right away
• сначала люблю полистать... = I prefer first to flip through...

So the contrast is:

• not buy it immediately
• but first look through it

This pairing is very natural in Russian:

• Не отвечай сразу — сначала подумай.
• Вместо того чтобы сразу соглашаться, сначала прочитай условия.

Here люблю does not necessarily mean strong emotional love. Very often, люблю + infinitive means:

• I like to...
• I tend to...
• I prefer to... (depending on context)

So:

• я люблю полистать её и посмотреть оглавление
  means something like
  I like to flip through it and look at the table of contents first.

This is a common use:

• Я люблю гулять вечером. = I like walking in the evening.
• Я люблю сначала всё проверить. = I like to check everything first.

In this sentence, люблю gives the sense of a personal habit or preference.

Both полистать and посмотреть are perfective infinitives, and that makes sense because they refer to short, complete actions done before buying.

• листать = to leaf through / flip through (process)

• полистать = to flip through for a while, have a look through

• смотреть = to look, watch (process)
• посмотреть = to look at, take a look, check

In this sentence, the speaker means:

• first flip through it a bit
• and take a look at the table of contents

These are seen as brief, bounded actions, so perfective is very natural.

If you used the imperfective forms:

• люблю листать её и смотреть оглавление

that would sound more like ongoing process or repeated activity in a more general way. It is not impossible, but полистать and посмотреть fit the idea better: do these quick checking actions before buying.

No, полистать is more specific.

It comes from листать, which literally means to turn pages / leaf through.

So полистать книгу means:

• to flip through a book
• to leaf through it
• to browse through it briefly

It does not mean:

• to read the whole book (прочитать)
• necessarily to inspect it carefully from start to finish

It suggests a quick physical browsing of the pages.

Examples:

• Я взял журнал полистать. = I picked up the magazine to flip through it.
• Перед покупкой я люблю полистать книгу. = Before buying, I like to leaf through a book.

Её here means it, referring to книгу.

Because книга is feminine, the pronoun is feminine too:

• книга → её

In the sentence:

• полистать её = to flip through it

Grammatically, её is in the accusative, but for this pronoun the accusative and genitive forms are the same in spelling:

• nominative: она
• accusative/genitive: её

So the pronoun agrees in gender with книга, even though in English we just say it.

Both are direct objects, so they are in the accusative case.

• покупать книгу = to buy a book
• посмотреть оглавление = to look at the table of contents

Why the forms differ:

• книга is a feminine noun ending in -а, so accusative singular becomes книгу
• оглавление is neuter and inanimate, and its accusative singular looks the same as the nominative: оглавление

So:

• nominative: книга → accusative: книгу
• nominative: оглавление → accusative: оглавление

Оглавление means table of contents.

It is the list of chapter or section titles in a book.

Russian also has содержание, which can sometimes also mean contents. In practice:

• оглавление is the more specific word for the table of contents in a book
• содержание can mean contents but also has other meanings, such as content, substance, or maintenance/upkeep, depending on context

So in a book-related sentence like this, оглавление is very clear and natural.

Both are possible, but they emphasize things a little differently.

• Я сначала люблю полистать её...
  emphasizes the sequence early: first, I like to...
• Я люблю сначала полистать её...
  puts люблю earlier and sounds like: I like first to flip through it...

Russian word order is flexible, and adverbs like сначала can move around. The version in your sentence is very natural because it sets up the contrast with сразу earlier:

• вместо того чтобы сразу покупать...
• я сначала люблю...

So the sentence has a nice balance:

• not immediately buy
• first browse

Yes. Russian offers several natural alternatives.

For example:

• Я не люблю сразу покупать книгу — сначала мне нравится полистать её и посмотреть оглавление.
• Прежде чем купить книгу, я люблю сначала полистать её и посмотреть оглавление.
• Перед тем как купить книгу, я люблю её сначала полистать и посмотреть оглавление.

These all express a similar idea:

• I don’t like buying a book right away
• first I want to browse it and check the table of contents

Your original sentence is perfectly natural, but these alternatives may feel easier to parse for a learner.