Quiero ponerme la camiseta azul claro para salir.

Because ponerme means to put on myself.

The base verb is poner = to put.
When you talk about putting clothes on yourself, Spanish normally uses the reflexive form ponerse.

So:

• Quiero poner la camiseta = I want to put the T-shirt down / place it
• Quiero ponerme la camiseta = I want to put the T-shirt on

The me shows that the action happens to the speaker themself.

Yes. That is also correct.

With a verb like querer followed by an infinitive, the reflexive pronoun can usually go in either place:

• Quiero ponerme la camiseta...
• Me quiero poner la camiseta...

Both mean the same thing.
The version in your sentence, Quiero ponerme..., is very common and natural.

In Spanish, with clothes and body parts, the definite article is often used instead of a possessive when it is already obvious whose item it is.

So Spanish prefers:

• Me pongo la camiseta = I put on my T-shirt

rather than:

• Me pongo mi camiseta

Using mi is possible, but it usually adds emphasis, contrast, or clarification, for example if you mean my T-shirt, not someone else’s.

In Spain, camiseta usually means T-shirt.

It can also sometimes refer to a sports shirt or jersey depending on context, but the basic everyday meaning is T-shirt.

Compare:

• camiseta = T-shirt
• camisa = shirt, usually not a T-shirt
• jersey = sweater/jumper in Spain

So here la camiseta azul claro most naturally means the light blue T-shirt.

Because in Spanish, adjectives usually come after the noun.

So:

• la camiseta azul claro = the light blue T-shirt

This is the normal order:

• noun: camiseta
• adjective/description: azul claro

Putting the colour before the noun would sound unusual here.

Because claro is describing the colour azul, not the noun camiseta directly.

So the phrase works as a set colour expression:

• azul claro = light blue

You do not change it to match camiseta here:

• la camiseta azul claro ✅
• la camiseta azul clara ❌

A good way to think of it is that azul claro behaves like one colour label: light blue.

It means something like to go out or for going out.

In this sentence, salir most likely means to go out, for example leaving the house or going out socially.

So:

• Quiero ponerme la camiseta azul claro para salir
  = I want to put on the light blue T-shirt to go out.

It gives the purpose of the action: I want to wear that shirt because I’m going out.

Yes. Salir can mean:

• to leave
• to go out
• to go out socially

The exact meaning depends on context.

In this sentence, without more context, many learners will understand it as go out, but it could also simply mean go out of the house. Spanish leaves that open unless the context makes it clearer.

Not in exactly the same way.

• ponerme = to put on
• llevar = to wear / have on

So:

• Quiero ponerme la camiseta azul claro = I want to put on the light blue T-shirt
• Quiero llevar la camiseta azul claro = I want to wear the light blue T-shirt

The first focuses on the action of getting dressed.
The second focuses more on the choice of clothing.

Sometimes, but the meaning would be a bit different.

• vestirme = to get dressed / dress myself
• ponerme la camiseta = to put on the T-shirt

So vestirme is more general, while ponerme points to a specific item of clothing.

For example:

• Quiero vestirme para salir = I want to get dressed to go out
• Quiero ponerme la camiseta azul claro para salir = I want to put on the light blue T-shirt to go out

If you want to mention the exact garment, ponerme is the better choice.

Quiero is perfectly natural here. It usually means I want to.

Depending on what you mean, you could also say:

• Voy a ponerme la camiseta azul claro para salir = I’m going to put on the light blue T-shirt to go out
• Me voy a poner la camiseta azul claro para salir = same meaning
• Prefiero ponerme la camiseta azul claro para salir = I prefer to put on the light blue T-shirt to go out

So quiero expresses desire or intention, while other options can sound more like a plan or preference.