Best filter to use for modifying custom fields on a post?

Ok, this is actually about the output as you said in your comment.

I suppose you know, you can do modification like this:

// assumed a single result is returned as string
$your_post_meta = get_post_meta( get_the_ID(), 'your_post_meta', true );
// lets add something
$your_modified_post_meta="My post meta: " . $your_post_meta;

So far so obvious I would say – depending on the return value might be an array you can do pretty much any modification possible for the type of data, but that would be a different likely PHP heavy topic.

Of course you are actually asking about a hook that can be used to do such things. To retrieve your post meta you are using get_post_meta() – source – I assume, which is a wrapper for get_metadata() – source. Inside get_metadata() we find the filter hook get_{$meta_type}_metadata – source – it is variable, depending on the $meta_type, which means for post meta(s) it is get_post_metadata.

It can be used like this:

add_filter(
    'get_post_metadata',
    'wpse162923_change_post_meta_out'
);
function wpse162923_change_post_meta_out(
    $check,
    $object_id,
    $meta_key,
    $single
) {
    if ( $meta_key == 'your_post_meta' ) {
        $your_post_meta = get_post_meta(
            $object_id,
            'your_post_meta',
            $single
        );
        $check =
            'My post meta: '
            . $your_post_meta;
    }
    return $check;
}

Note: the above is just exemplary, so make it fit to your needs.