Даже если книга недорогая, мне важно, чтобы её было приятно держать в руках.

Даже если means even if.

It introduces a condition that does not change the main point:

• Даже если книга недорогая... = Even if the book is inexpensive...

So the speaker is saying: the price may be low, but that is not enough; the physical feel of the book still matters.

In the present tense, Russian usually omits the verb быть (to be).

So:

• книга недорогая literally looks like book inexpensive
• but it means the book is inexpensive

This is completely normal in Russian.
You would only see forms of быть in the past or future, or in special styles/usages.

Because недорогая agrees with книга, which is:

• feminine
• singular
• nominative

So the adjective must also be feminine singular nominative:

• книга → недорогая

Compare:

• недорогой стол = an inexpensive table
• недорогая книга = an inexpensive book
• недорогое издание = an inexpensive edition

Both can relate to low price, but the nuance is different.

• недорогая = inexpensive, not expensive
  Neutral and often positive or matter-of-fact.
• дешёвая = cheap
  This can sound more negative and may suggest low quality.

Here the speaker is talking about price without insulting the book’s quality, so недорогая is the more natural choice.

Literally, мне важно is something like to me, it is important.

Russian often uses the dative for the person who experiences a feeling, attitude, or judgment:

• мне важно = it is important to me
• мне трудно = it is difficult for me
• мне интересно = it is interesting to me

So мне is not the subject in the English sense. It is the experiencer.

Чтобы introduces the situation that the speaker wants, values, or considers necessary.

So:

• мне важно, чтобы... = it is important to me that...
• or more naturally here: what matters to me is that...

This is a very common pattern in Russian:

• Мне нужно, чтобы он пришёл. = I need him to come.
• Важно, чтобы всё было удобно. = It is important that everything be comfortable/convenient.

This is a very common feature of clauses with чтобы.

After чтобы, Russian often uses a verb form that looks like the past tense, because the clause expresses something desired, expected, or non-factual, not a plain present fact.

So:

• чтобы её было приятно держать в руках
  = so that it would be pleasant/nice to hold it

Without чтобы, a plain statement is also possible:

• Её приятно держать в руках. = It is pleasant to hold it.

But after чтобы, было is the natural form.

Because приятно here does not describe the book directly as an agreeing adjective.

It is an impersonal predicative word meaning something like:

• it is pleasant
• it feels nice

So the structure is:

• её было приятно держать = it was/would be pleasant to hold it

If you said приятная книга, that would mean a pleasant book, describing the book itself.
But here the meaning is about the experience of holding it, not simply a property listed like an adjective.

Её here is the accusative form of the feminine pronoun она, referring back to книга.

So:

• книга = the book
• её держать = to hold it

In this sentence, её is the direct object of держать.

A learner should also note that её can have more than one job in Russian:

• её книга = her book
• я вижу её = I see her / it

Here it clearly means it, referring to книга.

Держать is imperfective, and that fits the meaning well.

The sentence is about the general feel or ongoing experience of holding the book in your hands, not one single completed action.

• держать = to hold
• подержать = to hold for a little while / to try holding

Here the speaker means something like:

• it should feel good in the hands
• it should be nice to hold

So the imperfective держать is the natural choice.

В руках literally means in the hands.

Russian normally uses the plural in this expression:

• держать в руках = to hold in one’s hands

This is idiomatic and very common. English also often uses the plural: in your hands.

Also notice that Russian does not need a possessive word here:

• держать в руках
  not necessarily
• держать в своих руках

The possessive is understood from context.

Here it is basically literal, but it is also a very common fixed expression.

In this sentence it means the physical experience of holding the book:

• its weight
• texture
• cover
• size
• overall hand-feel

So the speaker is saying that even a cheap/inexpensive book should still feel good physically when you hold it.

Yes, Russian word order is flexible, but the version here is very natural.

Current sentence:

• Даже если книга недорогая, мне важно, чтобы её было приятно держать в руках.

This order clearly presents:

1. the concession/condition
2. the speaker’s attitude
3. the important quality

You could move things around for emphasis, but this version sounds balanced and standard.

There are two subordinate clauses, so commas are required.

1. Даже если книга недорогая, ...
   The clause with если is separated from the main clause.

2. мне важно, чтобы её было приятно держать в руках
   The clause with чтобы is also separated by a comma.

So the punctuation reflects the structure very clearly:

• concessive/conditional clause
• main clause
• subordinate clause of what is important

Yes, that is close in meaning, but the Russian phrasing is a bit more natural and less direct.

• мне важно = it matters to me
• чтобы её было приятно держать в руках = that it be pleasant to hold in the hands

So the overall tone is:

• not exactly a strong demand
• more a statement of personal standards or preference

A smooth English equivalent would be something like:

• Even if a book is inexpensive, it matters to me that it feels nice to hold.