What's the MOST right way based on Wordpress ideology to exchange user text within the publish content?

Example: I wish to replace [b] User Text[/b] To <strong> User text</strong> when text made within the browser

Will I need filter? Will I need Short code API? Or it's perfectly fine to make use of PHP text changing functions?

A little code sample is going to be highly appreciated.

I'd make use of the Shortcode API, your code for that functions.php would look something similar to this:

function shortcode_b_replace($atts, $content = null) {
    return '<strong>'.$content.'</strong>';
add_shortcode("b", "shortcode_b_replace");