As described in the Child Themes entry in the codex:

TIP FOR THEME DEVELOPERS. The fact that a child theme’s functions.php is loaded first means that you can make the user functions of your theme pluggable —that is, replaceable by a child theme— by declaring them conditionally.

if ( ! function_exists( 'theme_special_nav' ) ) {
function theme_special_nav() {
    //  Do something.
    }
}

In that way, a child theme can replace a PHP function of the parent by simply declaring it beforehand.

If the theme you are developing will be released for general usage (i.e., you will be submitting it to the wordpress.org repository), then you should definitely build in capabilities that allow others who are building child themes based on your theme to override certain features of your theme.

Which features you allow to be override is up to you, and you need not build in the capability to override every function/feature.

Another thing you can do to make it easier for others to build child themes from your theme is to incorporate theme-specific actions/filters where appropriate.

As to your OOP vs procedural question: it really comes down to personal style.

To build an OOP style theme, you can make judicious use of final methods. That is, when a procedural style should not wrap a function in if (!function_exists(...)) { then you’d make that method final, etc.

Edit

The answer to this other WPSE question provides more context for developing OOP style themes.