En la playa prefiero llevar sombrero y no gorra.

Because en is used here to mean at/on the beach as a location.

• en la playa = at the beach / on the beach
• a la playa usually means to the beach, showing movement or destination

So:

• En la playa prefiero... = At the beach, I prefer...
• Voy a la playa = I’m going to the beach

Prefiero is the first person singular form of preferir, which means to prefer.

So:

• preferir = to prefer
• prefiero = I prefer

This verb is a stem-changing verb in the present tense:

• yo prefiero
• tú prefieres
• él/ella prefiere
• nosotros preferimos
• vosotros preferís
• ellos prefieren

The change is e → ie in most forms, but not in nosotros or vosotros.

After prefiero, Spanish uses the infinitive when talking about preferring to do something.

So:

• prefiero llevar = I prefer to wear / to take
• not prefiero llevo

This is like English I prefer to wear...

Other examples:

• Prefiero comer en casa. = I prefer to eat at home.
• Prefiero ir mañana. = I prefer to go tomorrow.

Here, llevar means to wear.

This verb is very common in Spanish and can mean different things depending on context:

• llevar una mochila = to carry a backpack
• llevar gafas = to wear glasses
• llevar sombrero = to wear a hat

In this sentence, because the words are sombrero and gorra, it clearly means to wear.

In Spain:

• sombrero = a hat, usually with a fuller brim
• gorra = a cap, especially one with a visor, like a baseball cap

So the sentence contrasts two different types of headwear:

• sombrero = hat
• gorra = cap

A learner might expect sombrero to mean a specifically Mexican-style hat, but in Spanish it is the general word for hat.

In Spanish, when talking generally about clothing or things someone prefers to wear, the article is often omitted.

So:

• prefiero llevar sombrero = I prefer wearing a hat / hats
• no gorra = not a cap / not caps

This sounds more general, not about one specific hat or one specific cap.

If you said:

• prefiero llevar un sombrero y no una gorra

that would also be possible, but it can sound a bit more specific or more focused on the singular item.

Spanish often leaves out the article in these general statements more naturally than English does.

Y no gorra literally means and not a cap.

Here, y no... is a simple way to contrast two options:

• prefiero llevar sombrero y no gorra = I prefer to wear a hat and not a cap

Spanish often uses y no where English might use:

• and not
• rather than
• instead of

You could also express the contrast in other ways, for example:

• prefiero llevar sombrero, no gorra
• prefiero llevar sombrero en vez de gorra

But y no gorra is a natural short contrast.

Yes, but it means something slightly different in structure.

• Prefiero llevar sombrero y no gorra = I prefer to wear a hat, not a cap
• Prefiero un sombrero a una gorra = I prefer a hat to a cap

The original sentence focuses on the action of wearing.
The alternative focuses more directly on choosing one item over the other.

Both are valid, but they are built differently.

Yes, both are possible.

• En la playa prefiero llevar sombrero y no gorra.
• Prefiero llevar sombrero y no gorra en la playa.

Putting En la playa first gives the setting first: At the beach...

This is very common in Spanish. The speaker highlights the context before the main statement.

The second version is also grammatical, but the first one may sound a bit more natural if the beach setting is what you want to introduce first.

Yes, gorra is feminine:

• la gorra
• una gorra

A common clue is that many nouns ending in -a are feminine, though not always.

In this sentence, even though there is no article before gorra, you would still need feminine agreement if you added one:

• no una gorra
• la gorra roja

By contrast:

• el sombrero
• un sombrero

So sombrero is masculine and gorra is feminine.

Yes, usar is possible, but llevar is usually more natural for clothing and accessories.

• llevar sombrero = to wear a hat
• usar sombrero = to use/wear a hat

In many contexts, Spanish prefers llevar for what someone has on their body.

So the original sentence sounds very natural:

• prefiero llevar sombrero...

Using usar would still be understandable, but it may sound less idiomatic in this case.

It would be understood perfectly across the Spanish-speaking world.

The vocabulary is standard:

• playa
• preferir
• llevar
• sombrero
• gorra

One small cultural note: in different regions, people may have slightly different associations with sombrero or may use other words for certain kinds of hats, but the sentence itself is completely standard and clear in Spain and elsewhere.