Поначалу я хотела купить роман сразу, но вскоре решила сначала проверить оглавление.

Because the speaker is female.

In the Russian past tense, verbs agree with the subject in gender and number:

• хотел = a man wanted
• хотела = a woman wanted
• решил = a man decided
• решила = a woman decided

So я хотела and решила show that the speaker is a woman.

Russian often omits the subject when it is already clear from context.

Here, the subject in both parts is the same person: я. So after но, Russian does not need to repeat it:

• Поначалу я хотела...
• но вскоре решила...

This is very natural. You could say но я вскоре решила, but it would sound more explicit or slightly more emphatic.

They are similar, but not identical.

• поначалу = at first / initially / in the beginning
• сначала = first / first of all / before doing something else

In this sentence:

• Поначалу refers to the speaker’s initial idea
• сначала проверить оглавление means she decided to check the table of contents first, before buying

So the sentence uses two different kinds of first:

1. At first, initially → поначалу
2. First, before the next action → сначала

That is why both can appear in the same sentence without being repetitive.

Сразу means right away / immediately / straight away.

So:

• купить роман сразу = buy the novel immediately

By contrast, сначала means first in the sense of before doing something else:

• сначала проверить оглавление = first check the table of contents

So:

• сразу focuses on immediacy
• сначала focuses on sequence

They are not the same.

Because купить is the perfective form, which presents the action as a single completed whole: to buy.

• купить = to buy, to make the purchase
• покупать = to be buying / to buy habitually / to buy in general

After verbs like хотеть and решить, Russian often uses the perfective infinitive when talking about a specific intended result:

• хотела купить = she wanted to buy
• решила проверить = she decided to check

In this sentence, she is talking about one specific novel and one possible purchase, so купить is the natural choice.

For the same reason: проверить is perfective and refers to a single completed check.

• проверить = to check, to look through once and get the result
• проверять = to be checking / to check repeatedly / to check in general

Here she decided on one concrete action: first check the table of contents. So the perfective проверить fits best.

It is in the accusative, but for an inanimate masculine singular noun, the accusative looks exactly like the nominative.

• nominative: роман
• accusative: роман

So in купить роман, роман is the direct object and is grammatically accusative, even though the form does not change.

Compare with an animate masculine noun:

• я вижу брата = I see my brother

There the accusative is different.

Because оглавление is a neuter inanimate noun, and for such nouns the accusative singular is the same as the nominative singular.

• nominative: оглавление
• accusative: оглавление

So проверить оглавление means to check the table of contents, with оглавление as the direct object.

Вскоре means soon / shortly afterward / before long.

In this sentence it shows that after her initial thought, she changed her mind fairly soon:

• но вскоре решила... = but soon she decided...

It connects naturally with поначалу:

• At first she wanted one thing,
• but soon she decided something else.

Because но is a coordinating conjunction meaning but, and it joins two clauses:

1. Поначалу я хотела купить роман сразу
2. но вскоре решила сначала проверить оглавление

Russian, like English, normally puts a comma before но when it connects clauses.

Russian word order is fairly flexible, but the original order sounds natural and clear.

The sentence is:

• Поначалу я хотела купить роман сразу, но вскоре решила сначала проверить оглавление.

This order highlights the timeline well:

• Поначалу = initial stage
• сразу = immediate purchase
• вскоре = soon afterward
• сначала = first check before buying

Some variations are possible, for example:

• Поначалу я хотела сразу купить роман...
• Но вскоре я решила сначала проверить оглавление...

These are also grammatical, but the emphasis shifts slightly.

Because verbs like хотеть (to want) and решить (to decide) are commonly followed by an infinitive in Russian, just like in English:

• хотела купить = wanted to buy
• решила проверить = decided to check

Russian does not need a separate word like English to before the second verb. The infinitive form itself does the job:

• купить
• проверить

So the structure is very normal:

• я хотела купить...
• я решила проверить...