How to selected which tags to print, instead of printing the whole tag list?

By get_the_tags() you receive an array of tags attached to the current post. So you could do the following:

$tags = get_the_tags();
$tag_ids_to_print = array( 1, 2, 3 ); //List of Tag IDs which you want to be printed

$print_tags = array();
if( is_array( $tags ) ){
    foreach( $tags as $tag ){
        if( in_array( $tag->term_id, $tag_ids_to_print ) )
            $print_tags[] = $tag;
    }
}

$tag_list="";
if( count( $print_tags ) > 0 ){
    //Execute only, when tags found
    $i = 0;
    foreach( $print_tags as $tag ){
        if( $i == 1 ) $tag_list .= ', ';
        $tag_list .= '<a href="' . get_tag_link( $tag->term_id ) . '">' . $tag->name . '</a>';
        $i = 1;
    }
}

Docs:

https://codex.wordpress.org/Function_Reference/get_the_tags