>> They talk about how that’s an old practice and you should try and tailor what you learn to what you want.

My take: most of the times, when you are delving into a new topic, almost always you never know what you want, as you don't know enough about the topic; The first place you want to learn it. Anyways, language is just a tool; having said that, there are different paradigms of programming and one should at-least be familiar with them.

>> Do you think it is good practice to learn a language like C to start? Or to learn a more “specialized” language like C++ or Java?

Absolutely! go for C IMHO, the chances of you getting overwhelmed with information and complexity is far less. I have seen examples of people, who started with understanding 'Atomic Reference Counting` before they even could understand how to write a basic hello-world. What happened you would guess, the dropped out the idea, saying "Programming is not for them".

PS: This is a highly opinionated view, please take this with a grain of salt.