Learn Hardcore Portuguese (Brazil): Eu quero escolher o curso certo.

Keeping eu is common and can add clarity or emphasis (especially when contrasting: Eu quero..., mas ele não quer.).
Dropping eu sounds a bit more neutral or informal in everyday speech.

So you can safely say either; the meaning is the same.

Why is it o curso certo and not um curso certo or just curso certo?

O is the definite article (the), and it shows you are talking about a specific, known course:

o curso certo = the right course (the specific one that will be right for me)

If you say:

um curso certo = a right course / some appropriate course (one of several possible good options, not a specific one in mind)

And:

curso certo without any article would normally sound incomplete or very stylized. In standard sentences, singular countable nouns usually take an article (o / a / um / uma) unless there is a special reason not to.

So in most natural contexts, o curso certo is what you want here.

Why does certo come after curso? Could I say o certo curso?

In Portuguese, adjectives usually come after the noun:

curso certo = right / correct course

When you put some adjectives before the noun, the meaning changes. With certo:

um certo curso ≈ a certain course / some particular course (you don’t want to say exactly which one)
o certo curso is unusual; people would understand, but it does not mean the right course.

So:

o curso certo = the right course (correct, appropriate)
um certo curso = a certain course (unspecified, vague)

For the idea of "right/correct," keep certo after the noun.

Is Eu quero escolher too direct or rude in Brazilian Portuguese? Should I say Eu gostaria de escolher instead?

Eu quero escolher o curso certo is not rude by itself; it is normal, especially:

when talking about yourself and your plans: Eu quero escolher o curso certo para mim.
among friends and family
in informal contexts

However, in requests to strangers or in very polite situations, Brazilians often soften quero:

Eu gostaria de escolher o curso certo. (literally I would like to choose...)
Eu queria escolher o curso certo. (imperfect tense used as a softener, very common in speech)

So:

Neutral / direct: Eu quero escolher...
More polite / softer: Eu gostaria de escolher... or Eu queria escolher...

The sentence in your example is perfectly fine; just adjust the verb in more formal or service situations.

Why is the verb querer in the form quero here? How is it conjugated?

Quero is first person singular, present tense of querer.

Present tense of querer:

eu quero – I want
você / ele / ela quer – you (sg.) / he / she wants
nós queremos – we want
vocês / eles / elas querem – you (pl.) / they want

So in Eu quero escolher o curso certo, quero matches eu. It is slightly irregular in other tenses, but this present tense is very common and good to memorize.

What is the role of escolher here? Do I need a preposition between querer and escolher?

Escolher is in the infinitive, meaning to choose. It works as the complement of querer:

querer + infinitive = to want to do something
- quero escolher – I want to choose
- queremos viajar – we want to travel
- ela quer estudar – she wants to study

You do not use a preposition between querer and the infinitive:

✔ quero escolher o curso certo
✘ quero de escolher o curso certo

Escolher itself can take a direct object:

escolher o curso certo – to choose the right course

It can also be used with entre when you mention options:

escolher entre dois cursos – to choose between two courses.

How would I say “I don’t want to choose the right course”?

Put não directly before the conjugated verb:

Eu não quero escolher o curso certo.
(Dropping eu is also fine:) Não quero escolher o curso certo.

There is just a single não; you do not add extra negation on the object.

How do I pronounce Eu quero escolher o curso certo in Brazilian Portuguese?

One approximate, Brazil‑oriented pronunciation (using English-like spelling) is:

Eu – like eh-oo said quickly: [ehw]
quero – KEH-roo (stress on KE; the r is a light tap, like the tt in better in American English)
escolher – roughly es-co-LYER
- es like es in escape
- co like co in coffee
- lh in -lher similar to the lli in million, then a Brazilian r at the end (often like a soft h, especially in Rio and many other regions)
o – short oo sound, like the o in moment but shorter
curso – KOOR-soo (stress on KOOR)
certo – SEHRT-oo (stress on SEHR; r tapped, final o is quite short)

Put together in a natural flow (São Paulo/Rio style):

[ew 'kɛɾu isko'ʎe(h) u 'kuɾsu 'sɛɾtu]

Rhythm-wise, the main stresses fall on QUE‑ro, -LHER, CUR‑so, CER‑to.

How do I know that curso is masculine, and how does that affect o and certo?

In Portuguese, nouns have grammatical gender. Curso is masculine, and most nouns ending in -o are masculine.

Because curso is masculine singular:

The definite article must also be masculine singular: o curso.
The adjective must agree: certo (masculine singular).

Other forms:

Plural: os cursos certos – the right courses
Feminine equivalent:
- a matéria certa – the right subject
- as matérias certas – the right subjects

So article and adjective always follow the noun’s gender and number.

Could I use another word instead of curso, like matéria or disciplina?

Yes, but the meaning changes slightly:

curso – usually a course of study: a program, degree, long course, or training (e.g. curso de medicina, curso de inglês).
matéria – a subject or school subject (math, history, etc.), especially in everyday speech at school level.
disciplina – also subject, but more formal or academic (used in university course catalogs, syllabi, etc.).

So:

Eu quero escolher o curso certo. – I want to choose the right program/course (e.g., major, degree, training course).
Eu quero escolher a matéria certa. – I want to choose the right subject (one particular class, like chemistry).

You choose the noun based on what kind of “course” you mean.

If I want to say “I’m going to choose the right course” (a plan), should I still use quero?

No. If you want to emphasize a future plan (not just desire), Brazilians normally use ir + infinitive:

Eu vou escolher o curso certo. – I’m going to choose the right course.

Compare:

Eu quero escolher o curso certo. – I want to choose the right course. (desire/intention)
Eu vou escolher o curso certo. – I am going to choose the right course. (plan/decision)

There is also a simple future tense:

Eu escolherei o curso certo.

But in Brazilian Portuguese this form is much less common in everyday speech than vou escolher.

Can I change the word order, like Eu quero o curso certo escolher?

No. In Portuguese the normal word order is Subject – Verb – Object, and you should keep the infinitive escolher directly after quero:

✔ Eu quero escolher o curso certo.

Placing the verb at the end:

✘ Eu quero o curso certo escolher.

sounds very unnatural and is wrong in standard modern Portuguese.

You can sometimes move the object to the front for emphasis:

O curso certo eu quero escolher.

but that is marked and emphatic, not the neutral way to say it. For regular use, stick with Eu quero escolher o curso certo.

Can I say o curso correto instead of o curso certo? Is there a difference?

You can say o curso correto, and people will understand, but there is a nuance:

o curso certo – the right/appropriate course (most idiomatic in this context; sounds very natural).
o curso correto – the correct course (more formal or focused on correctness, as in correct answer / correct procedure).

In everyday speech about choices in life, career, studies, Brazilians normally prefer curso certo. Curso correto is not wrong, just less common and a bit more technical or formal.